Probability Questions and Answers

Suppose X is a continuous random variable Then the probability that X is exactly 6 is P X 6

Given the uniform distribution below find the probability of the shaded region Give your answer in fraction form 19

A survey found that women s heights are normally distributed with mean 63 6 in and standard deviation 2 5 in A branch of the military requires women s heights to be between 58 in and 80 in a Find the percentage of women meeting the height requirement Are many women being denied the opportunity to join this branch of the military because they are too short or too tall b If this branch of the military changes the height requirements so that all women are eligible except the shortest 1 and the tallest 2 what are the new height requirements Click to view page 1 of the table Click to view page 2 of the table a The percentage of women who meet the height requirement is Round to two decimal places as needed Are many women being denied the opportunity to join this branch of the military because they are too short or too tall O A No because only a small percentage of women are not allowed to join this branch of the military because of their height O B Yes because the percentage of women who meet the height requirement is fairly large OC No because the percentage of women who meet the height requirement is fairly small OD Yes because a large percentage of women are not allowed to join this branch of the military because of their height b For the new height requirements this branch of the military requires women s heights to be at least in and at most in Bound to one donimol pia

A clinical test on humans of a new drug is normally done in three phases Phase I is conducted with a relatively small number of healthy volunteers For example a phase I test of a specific drug involved only 5 subjects Assume that we want to treat 5 healthy humans with this new drug and we have 10 suitable volunteers available Complete parts a through c below a If the subjects are selected and treated in sequence so that the trial is discontinued if anyone displays adverse effects how many different sequential arrangements are possible if 5 people are selected from the 10 that are available Choose the correct answer below OA 252 OB 3 628 800 OC 30 240 OD 120 b If 5 subjects are selected from the 10 that are available and the 5 selected subjects are all treated at the same time how many different treatment groups are possible different treatment groups possible c If 5 subjects are randomly selected and treated at the same time what is the probability of selecting the 5 youngest subjects P selecting the 5 youngest subjects Type an integer or a simplified fraction There are

Points 0 of 1 The probability of having at least two male children is Type an integer or a simplified fraction Save You select a family with three children If M represents a male child and F a female child the set of equally likely outcomes for the children s genders is shown below Find the probability of selecting a family with at least two male children MMM MMF MFM MFF FMM FMF FFM FFF

A water taxi carries passengers from harbor to another Assume that weights of passengers are normally distributed with a mean of 184 lb and a standard deviation of 35 lb The water taxi has a stated capacity of 25 passengers and the water taxi was rated for a load limit of 3500 lb Complete parts a through d below a Given that the water taxi was rated for a load limit of 3500 lb what is the maximum mean weight of the passengers if the water taxi is filled to the stated capacity of 25 passengers The maximum mean weight is 140 lb Type an integer or a decimal Do not round b If the water taxi is filled with 25 randomly selected passengers what is the probability that their mean weight exceeds the value from part a The probability is 1 Round to four decimal places as needed c If the weight assumptions were revised so that the new capacity became 20 passengers and the water taxi is filled with 20 randomly selected passengers what is the probability that their mean weight exceeds 175 lb which is the maximum mean weight that does not cause the total load to exceed 3500 lb The probability is 0 8749 Round to four decimal places as needed d Is the new capacity of 20 passengers safe Since the probability of overloading is the new capacity to be safe enough

When testing for current in a cable with ten color coded wires the author used a meter to test five wires at a time How many different tests are required for every possible pairing of five wires The number of tooto

If radio station call letters must begin with either K or W and must include either two or three additional letters how many different possibilities are there There are different possibilities Simplify your answer

When a man observed a sobriety checkpoint conducted by a police department he saw 672 drivers were screened and 7 were arrested for driving while intoxicated Based on those results we can estimate that P W 0 01042 where W denotes the event of screening a driver and getting someone who is intoxicated What does P W denote and what is its value What does P W represent OA P W denotes the probability of screening a driver and finding that he or she is not intoxicated OB P W denotes the probability of screening a driver and finding that he or she is intoxicated OC P W denotes the probability of a driver passing through the sobriety checkpoint OD P W denotes the probability of driver being intoxicated P W Round to five decimal places as needed

A research center poll showed that 83 of people believe that it is morally wrong to not report all income on tax returns What is the probability that someone does not have this belief The probability that someone does not believe that it is morally wrong to not report all income on tax returns is Type an integer or a decimal

Each of two parents has the genotype red blond which consists of the pair of alleles that determine hair color and each parent contributes one of those allele a child Assume that if the child has at least one red allele that color will dominate and the child s hair color will be red a List the different possible outcomes Assume that these outcomes are equally likely b What is the probability that a child of these parents will have the blond blond genotype c What is the probability that the child will have red hair color a List the possible outcomes OA red blond and blond red B red red and blond blond OC red red red blond blond red and blond blond OD red red red blond and blond blond b The probability that a child of these parents will have the blond blond genotype is Round to two decimal places as needed The probability that the child will have red hair color is

A boat capsized and sank in a lake Based on an assumption of a mean weight of 149 lb the boat was rated to carry 60 passengers so the load limit was 8 940 lb After the boat sank the assumed mean weight for similar boats was changed from 149 lb to 171 lb Complete parts a and b below a Assume that a similar boat is loaded with 60 passengers and assume that the weights of people are normally distributed with a mean of 179 8 lb anc a standard deviation of 39 1 lb Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 149 lb The probability is 1 Round to four decimal places as needed b The boat was later rated to carry only 13 passengers and the load limit was changed to 2 223 lb Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 171 so that their total weight is greater than the maximum capacity of 2 223 lb The probability is 0 7915 Round to four decimal places as needed Do the new ratings appear to be safe when the boat is loaded with 13 passengers Choose the correct answer below OA Because there is a high probability of overloading the new ratings do not appear to be safe when the boat is loaded with 13 passengers O B Because the probability of overloading is lower with the new ratings than with the old ratings the new ratings appear to be safe C Because there is a high probability of overloading the new ratings appear to be safe when the boat is loaded with 13 passengers D Because 179 8 is greater than 171 the new ratings do not appear to be safe when the boat is loaded with 13 passengers

Assume the readings on thermometers are normally distributed with a mean of 0 C and a standard deviation of 1 00 C Find the probability that a randomly selected thermometer reads between 1 06 and 0 09 and draw a sketch of the region Click to view page 1 of the table Click to view page 2 of the table Sketch the region Choose the correct graph below O A 1 06 0 09 O B 1 06 0 09 The probability is Round to four decimal places as needed Ly O C 1 06 0 09 Q G

An airliner carries 200 passengers and has doors with a height of 74 in Heights of men are normally distributed with a mean of 69 0 in and a standard deviation of 2 8 in Complete parts a through d a If a male passenger is randomly selected find the probability that he can fit through the doorway without bending The probability is 0 9629 Round to four decimal places as needed b If half of the 200 passengers are men find the probability that the mean height of the 100 men is less than 74 in The probability is 0 9999 Round to four decimal places as needed c When considering the comfort and safety of passengers which result is more relevant the probability from part a or the probability from part b Why OA The probability from part a is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height OB The probability from part b is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height OC The probability from part b is more relevant because it shows the proportion of male passengers that will not need to bend OD The probability from part a is more relevant because it shows the proportion of male passengers that will not need to bend

A survey found that women s heights are normally distributed with mean 62 8 in and standard deviation 2 3 in The survey also found that men s heights are normally distributed with mean 69 2 in and standard deviation 3 7 in Most of the live characters employed at an amusement park have height requirements of a minimum of 55 in and a maximum of 64 in Complete parts a and b below a Find the percentage of men meeting the height requirement What does the result suggest about the genders of the people who are employed as characters at the amusement park The percentage of men who meet the height requirement is 7 99 Round to two decimal places as needed Since most men the height requirement it is likely that most of the characters are

When two births are randomly selected the sample space for genders is bb bg gb and gg Assume that those four outcomes are equally likely Construct a table that describes the sampling distribution of the sample proportion of girls from two births Does the mean of the sample proportions equal the proportion of girls in two births Does the result suggest that a sample proportion is an unbiased estimator of a population proportion For the entire population 1 1 the probability of having a girl is assume the probability of having a boy is 2 affected by how many boys or girls have previously been born Determine the probabilities of each sample proportion Sample proportion of girls 0 0 5 1 and this is not 2 Probability 0 25 0 5 0 25 Type integers or simplified fractions Does the mean of the sample proportions equal the proportion of girls in two births 1 3 1 OA Yes both the mean of the sample proportions and the population proportion are OB Yes both the mean of the sample proportions and the population proportion are OC No the mean of the sample proportions and the population proportion are not equal D Yes both the mean of the sample proportions and the population proportion are 2 1

The ages years of three government officials when they died in office were 56 45 and 60 Complete parts a through d a Assuming that 2 of the ages are randomly selected with replacement list the different possible samples A 56 56 56 45 56 60 45 56 45 45 45 60 60 56 60 45 60 60 OB 56 56 56 45 56 60 45 45 45 60 60 60 C 56 45 56 60 45 60 OD 56 45 56 60 45 56 45 60 60 56 60 45 b Find the range of each of the samples then summarize the sampling distribution of the ranges in the format of a table representing the probability distribution Sample Range Probability

The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 7 8 cm a Find the probability that an individual distance is greater than 208 40 cm b Find the probability that the mean for 20 randomly selected distances is greater than 193 20 cm c Why can the normal distribution be used in part b even though the sample size does not exceed 30 a The probability is 0 0429 Round to four decimal places as needed b The probability is Round to four decimal places as needed

A water taxi carries passengers from harbor to another Assume that weights of passengers are normally distributed with a mean of 184 lb and a standard deviation of 35 lb The water taxi has a stated capacity of 25 passengers and the water taxi was rated for a load limit of 3500 lb Complete parts a through d below a Given that the water taxi was rated for a load limit of 3500 lb what is the maximum mean weight of the passengers if the water taxi is filled to the stated capacity of 25 passengers The maximum mean weight is 140 lb Type an integer or a decimal Do not round b If the water taxi is filled with 25 randomly selected passengers what is the probability that their mean weight exceeds the value from part a The probability is Round to four decimal places as needed

An airliner carries 200 passengers and has doors with a height of 74 in Heights of men are normally distributed with a mean of 69 0 in and a standard deviation of 2 8 in Complete parts a through d a If a male passenger is randomly selected find the probability that he can fit through the doorway without bending The probability is Round to four decimal places as needed

For bone density scores that are normally distributed with a mean of 0 and a standard deviatic of 1 find the percentage of scores that are a significantly high or at least 2 standard deviations above the mean b significantly low or at least 2 standard deviations below the mean c not significant or less than 2 standard deviations away from the mean a The percentage of bone density scores that are significantly high is Round to two decimal places as needed

When women were finally allowed to become pilots of fighter jets engineers needed to redesign the ejection seats because they had been originally designed for men only The ejection seats were designed for men weighing between 140 lb and 211 lb Weights of women are now normally distributed with a mean of 167 lb and a standard deviation of 45 lb Complete parts a through c below a If 1 woman is randomly selected find the probability that her weight is between 140 lb and 211 lb The probability is approximately Round to four decimal places as needed

When two births are randomly selected the sample space for genders is bb bg gb and gg Assume that those four outcomes are equally likely Construct a table that describes the sampling distribution of the sample proportion of girls from two births Does the mean of the sample proportions equal the proportion of girls in two births Does the result suggest that a sample proportion is an unbiased estimator of a population proportion For the entire population 1 1 assume the probability of having a boy is the probability of having a girl is and this is not affected by how many boys or girls have previously been born Determine the probabilities of each sample proportion Sample proportion of girls Probability ors or simplified fractions

The ages years of three government officials when they died in office were 56 45 and 60 Complete parts a through d a Assuming that 2 of the ages are randomly selected with replacement list the different possit samples A 56 56 56 45 56 60 45 56 45 45 45 60 60 56 60 45 60 60 B 56 56 56 45 56 60 45 45 45 60 60 60 OC 56 45 56 60 45 60 OD 56 45 56 60 45 56 45 60 60 56 60 45

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes Find the probability that a randomly selected passenger has a waiting time greater than 3 25 minutes Find the probability that a randomly selected passenger has a waiting time greater than 3 25 minutes Simplify your answer Round to three decimal places as needed

Given a normal population whose mean is 670 and whose standard deviation is 37 find each of the following A The probability that a random sample of 7 has a mean between 672 and 683 Probability B The probability that a random sample of 17 has a mean between 672 and 683 Probability C The probability that a random sample of 30 has a mean between 672 and 683 Probability

Assume that women s weights are normally distributed with a mean given by 143 lb and a standard deviation given by o 29 lb a If 1 woman is randomly selected find the probabity that her weight is between 113 lb and 176 lb b If 6 women are randomly selected find the probability that they have a mean weight between 113 lb and 176 lb c If 58 women are randomly selected find the probability that they have a mean weight between 113 lb and 176 lb

Suppose that the readings on the thermometers are normally distributed with a mean of 0 and a standard deviation of 1 00 C If 6 of the thermometers are rejected because they have readings that are too low but all other thermometers are acceptable find the reading that separates the rejected thermometers from the others

The combined math and verbal scores for students taking a national standardized examination for college admission is normally distributed with a mean of 750 and a standard deviation of 160 If a college requires a student to be in the top 40 of students taking this test what is the minimum score that such a student can obtain and still qualify for admission at the college answer round to the nearest integer

Question 3 6 pts The following table represents gas well completions during 1986 in North and South America Source American Gas Association 1987 Gas Facts p 50 a b c P D P N North America N South America N TOTALS P D and N P D and N P D and N P D and N P D or N P D or N P D or N P D or N Useful Formulas Rule 1 P A or B P A P B P A and B Rule 2 P A or B P A and B P A and B Rule 3 P A B P B Rule 4 P AB Dry D 14 131 404 14 535 Not dry D 31 575 2 563 34 138 P A XP BA RA XP BARA YB RA TOTALS 45 706 2 967 48 643 Note The sign means complement of an event

Question 3 6 pts The following table represents gas well completions during 1986 in North and South America Source American Gas Association 1987 Gas Facts p 50 a b c P D P N North America N South America N TOTALS P D and N P D and N P D and N P D and N P D or N P D or N P D or N P D or N Useful Formulas Rule 1 P A or B P A P B P A and B Rule 2 P A or B P A and B P A and B Rule 3 P A B P B Rule 4 P AB Dry D 14 131 404 14 535 Not dry D 31 575 2 563 34 138 P A XP BA RA XP BARA YB RA TOTALS 45 706 2 967 48 643 Note The sign means complement of an event

When we think of scientific data we might think of a signal from an instrument but data can be a lot of different things The type of data a researcher collects is based on his or her research question Identify the data that could be collected to aner each of the following research auaskane luau may select the data multiple times Choose Rate of students s completion of assignments Description of phytoplankton species Test Scores Mass of precipitate Response rate How does acid in sediment affect the grow Volume of acid rate of a bean plant Absorbance of light Changes of length of leaf over time Distance Pressure How does the browning of apples differ under different temperature conditions How does adding a strong acid affect the amount of precipitate calcium oxalate that is formed from milk source of calcium ions and almonds source of oxalate ions What are the seasonal variations on phytoplankton populations in English bay How well can an automated tool detect defects bugs in students programming assignments How well do students understand calculating mean and standard deviation Mass of phytoplankton Taste of the brown part of apples under different conditions Mass of apples under different conditions Measure the surface area of the brown part of the apple Difference between manual marking of assignments and automated marking of assignments Choose Choose

For the following report about a statistical study identify if possible a the population b the population parameter of interest c the sampling frame d the sample e the sampling method including whether or not randomization was employed f who if anyone was left out of the study and g any potential sources of bias you can detect and any problems you see in generalizing to the population of interest Researchers waited outside a bar they had randomly selected from a list of such establishments They rolled a twenty sided die and it came up 3 so they stopped the third adult who came out of the bar then every 15th adult after that and asked whether they thought drinking and driving was a serious problem a What is the population OA The population is all bars OB The population is the adults who came out of the bar OC The population is all adults who would visit a bar OD The population is the adults in the bar OE The population for the study is unclear b What is the population parameter of interest BERICH

Suppose a poll of 892 adults asked whether increasing domestic energy production or protecting the environment should be given a higher priority The results are shown to the right Suppose we select three people at random from this sample Complete parts a through d below a What is the probability that all three responded Protect environment Round to three decimal places as needed b What is the probability that none responded Equally Important Round to three decimal places as needed c What assumption must be made to compute these probabilities This question 2 point s possible OA The events occur simultaneously B The order of the events does not matter Submit test Response Increase production 408 Protect environment 404 42 Equally important No opinion Total 38 892 Number E

Suppose a poll of 892 adults asked whether increasing domestic energy production or protecting the environment should be given a higher priority The results are shown to the right Suppose we select three people at random from this sample Complete parts a through d below c What assumption must be made to compute these probabilities OA The events occur simultaneously OB The order of the events does not matter OC The events are disjoint OD The events are independent d Explain why that assumption is reasonable OA The people were selected at random Response Increase production 408 Protect environment 404 Equally important 42 No opinion Total 38 892 Number

As mentioned in the chapter opinion polling organizations contact their respondents by sampling random telephone numbers Although interviewers now can reach about 45 8 of U S households the percentage of those contacted who agree to cooperate with the survey has fallen from 43 2 in 1997 to only 6 3 in 2018 Pew Research Center Each household selected of course is independent of the others a What is the probability that the next house will be contacted and refuse to cooperate b What is the probability in 2018 of failing to contact a house or making contact and not getting them to agree to the interview c Show reasonable ways to calculate the probability in part b a The probability that the next house will be contacted and refuse to cooperate is Type an integer or a decimal rounded to four decimal places b The probability of failing to contact a house or making contact and not getting them to agree to the interview is Type an integer or a decimal rounded to for decimal places c Show reasonable ways to calculate the probability in part b Select all that apply Submit test A P contacted n not agree x 1 P contacted B P contacted n not agree 1 P contacted

An amusement park has opened a new roller coaster It is so popular that people are waiting for up to 3 hours for a 2 minute ride Concerned about how patrons who paid a large amount to enter the park and ride on the rides feel about this they survey every 15th male as they exit the park starting from a randomly selected male Complete parts a through d below b vvnat is the sampling frame OA all the male patrons of the park OB all the males who go to amusement parks OC all the male patrons who like roller coasters OD all the patrons of the park c is the sample likely to be representative of the population of interest OA Yes the sample is likely to be representative of everyone in the park OB No the sample is not likely to be representative of everyone who waited in line for the roller coaster OC No the sample is not likely to be representative of everyone in the park On Vor the comple is likely to ho ropocentative of overwone who waited in line for the roller coaster

C This question 2 point s possible In 1978 a popular science magazine reported that a study of women in Australia indicated that having sons shortened the lifespans of mothers by about 47 weeks per son but that daughters helped to lengthen the mothers lives The data came from church records from the period 1605 to 1887 Answer parts a through e below OA The parameter of interest is difference in average lifespan between sons and daughters OB The parameter of interest is difference in average lifespan between mothers of sons and mothers of daughters OC The parameter of interest is average numbers of sons and daughters OD The parameter of interest is difference in average lifespan of mothers in Australia e Identify the nature and scope of the conclusion regarding what the results may or may not indicate Submit test OA For this group having sons was associated with a decrease in lifespan of an average of 47 weeks per son while having daughters was associated with an unspecified increase in lifespan Without random assignment there is no way to know that having sons caused a decrease in lifespan OB For this group having children was associated with a decrease in lifespan of an average of 47 weeks per child Without random assignment there is no way to know that having sons caused a decrease in lifespan OC For this group having daughters was associated with an increase in lifespan of an average of 47 weeks per daughter while having sons was associated with an unspecified decrease in lifespan

in 1978 a popular science magazine reported that a study of women in Australia indicated that having sons shortened the lifespans of mothers by about 47 weeks per son but that daughters helped to lengthen the mothers lives The data came from church records from the period 1605 to 1887 Answer parts a through e below a Identify whether the above research is an observational study or an experiment The described research is an b Was the study retrospective or prospective observational study This is a c Identify The subje How were retrospective prospective d how they were selected 2 OA T www or the study OR The women were randomly selected

Are fat and calories in fast food related Here are the fat and calorie data for several brands of burgers Analyze the association between fat content and calories using correlation and scatterplots Fat g Calories O A Calories 700 T 23 426 300 10 Make a scatterplot for the data Choose the correct answer below F Fat g 50 32 584 5 33 588 37 567 OB What is the correlation coefficient for the data Calories 700 40 641 300 10 IC B Fat g 40 677 50 Q Q 44 660 O C Calories 700 T 300 10 Fat g 50 o O D Calories 700 300 10 F Fat g 50 O

Is there an association between time of year and the nighttime temperature in North Dakota A researcher assigned the numbers 1 365 to the days January 1 December 31 and recorded the temperature at 2 00 a m for each What might you expect the correlation between DayNumber and Temperature to be Explain Choose the correct answer below SCIEB OA Temperatures should be low in January increase through spring and into the summer months and then decrease again in the fall and winter Since there is a clear pattern the correlation should be near 1 OB Temperatures should be low in January increase through spring and into the summer months and then decrease again in the fall and winter Since the relationship is not linear the correlation should be near 0 OC Temperatures should be low in January increase through spring and into the summer months and then decrease again in the fall and winter Since there is a clear pattern the correlation should be near 1 O D Temperatures should be low in January and then increase throughout the rest of the year Since the relationship is positive and linear the correlation should be near 1

9 pts According to a study 67 of cars are some shade of grey white black grey or silver If we take a random sample of 25 cars find the following probabilities a None of them are a shade of gray 1 0 67 0 33 b All of them are a shade of gray 67 0 67 c Exactly 15 of them are a shade of gray

An analysis of the amount of fiber in grams and the potassium content in milligrams in servings of 77 breakfast cereals produced the regression model Potassium 35 24Fiber Explain what the slope means Choose the correct answer below Submit test OA The model predicts that cereals will have approximately 35 more grams of fiber for every additional milligram of potassium OB The model predicts that cereals will have approximately 35 more milligrams of potassium for every additional gram of fiber OC The model predicts that cereals will have approximately 24 more milligrams of potassium for every additional gram of fiber OD The model predicts that cereals will have approximately 24 more grams of fiber for every additional milligram of potassium

Question 9 of 15 Suppose X is a binomial random variable with 10 trials and success probability 0 60 Find the mean of X Answer Previous Answer 6

An experiment is to draw 1 card from a fair deck of playing cards a If you were to list the sample space how many equally likely outcomes would it have b Find the probability of getting a 7 Leave your answer as a fraction c Find the probability of not getting a diamond Leave your answer as a fraction d Find the probability of getting a spade Leave your answer as a fraction e Find the probability of getting a 7 or a club Leave your answer as a fraction

You roll two fair dice a If you were to list the sample space for this problem how many equally likely outcomes would there be b Find the probability of getting a sum of 9 Leave your answer as a fraction c Find the probability of getting a 5 on the first die Leave your answer as a fraction d Find the probability of getting a sum of 9 AND a 5 on the first die Leave your answer as a fraction e Find the probability of getting a sum of 9 OR a 5 on the first die Leave your answer as a fraction f Find the probability of getting doubles Leave your answer as a fraction g Find the probability of getting both dice to be odd numbers Leave your answer as a fraction h Find the probability of getting doubles AND both dice to be odd numbers Leave your answer as a fraction i Find the probability of getting doubles OR both dice to be odd numbers

Eyeglassomatic manufactures eyeglasses for different retailers They test to see how many defective lenses they made in a time period The folllowing table gives the type of defect and the number of lenses with that defect Assume categories are mutually exclusive Defect Type Scratch Right shaped small Flaked Wrong axis Chamfer wrong Crazing cracks Wrong shape Wrong PD Spots and bubbles Wrong height Right shape big Lost in lab intern Spots bubbles Frequency 5621 4672 1803 1418 1775 1561 1583 1550 1410 1123 1348 991 990 a Find the probability that a randomly selected defect from the table will be in the categor Right shaped small or the category Wrong axis Give your answer as a fraction Give your answer rounded to three decimal places b Find the probability that a randomly selected defect is not in the category Right shaped small Given your answer as a fraction Give your answer rounded to three decimal places

A fair coin is flipped three times a State the sample space List outcomes separated by commas Use notation like HTT to mean the first toss was heads the second toss was tails and the third toss was tails b Find the probability of getting exactly two heads Leave your answer as a fraction c Find the probability of getting at least 1 tail Leave your answer as a fraction d Find the probability of getting an odd number of tails Leave your answer as a fraction e Find the probability of getting all heads or all tails Leave your answer as a fraction f Find the probability of getting exactly two heads or exactly two tails Leave your answer as a fraction g Find the probability of not getting at least 1 tail Leave your answer as a fraction

In the game of roulette there is a wheel with spaces marked 0 through 36 and a space marked 00 a Find the probability of winning if you pick the number 26 and it comes up on the wheel Leave your answer as a fraction b Find the probability of an odd number coming up on the wheel Leave your answer as a fraction

The number of M Ms of each color that were found in a case with M Ms is given in the table below color Freq blue 286 brown green orange red yellow 243 220 219 117 346 a Find the probability that a randomly selected M M will be in the category blue or brown Give your answer as a fraction Give your answer rounded to three decimal places Give your answer rounded to three decimal places b Find the probability that a randomly selected M M is not in the category blue Given your answer as a fraction