# Probability Questions and Answers

Statistics

ProbabilityNote that an Ace is considered a face card for this problem In drawing a single card from a regular deck of 52 cards we have a P black and a Queen b P black or a 3 c P black and a face card d P Queen and a 3 e P face card or a number card

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ProbabilityTwo cards are drawn from a regular deck of 52 cards without replacement What is the probability that the first card is an ace of clubs and the second is black Answer Preview My Answers Submit Answers

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ProbabilityThe following table lists the joint probabilities associated with smoking and lung disease among 60 to 65 year old men Smoker Nonsmoker 0 05 0 66 Has Lung Disease 0 09 No Lung Disease 0 2 One 60 to 65 year old man is selected at random What is the probability of the following events A He is a smoker B He does not have lung disease C He has lung disease given that he is a smoker D He has lung disease given that he does not smoke

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ProbabilityThe age distribution for senators in the 104th U S Congress was as follows age under 40 40 49 50 59 60 69 70 and over no of senators 1 14 41 27 17 Consider the following four events A event the senator is under 40 B event the senator is in his or her 50s C event the senator is 40 or older D event the senator is under 60 Find the probability of each event given below a A or C b C and D c A d A and D e B and D

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ProbabilityGiven that P A 0 85 and P BA 0 22 find the joint probability P A and B P A and B

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ProbabilityAll that is left in a packet of candy are 6 reds 3 greens and 3 blues a What is the probability that a random drawing yields a green followed by a red assuming that the first candy drawn is put back into the packet Answer b Are the events green and red dependent Answer

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Probability1 point Suppose that X is an event and that P X 0 35 What is P X i e the probability that X will not occur Answer

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ProbabilityAn American roulette wheel has 38 slots two slots are numbered 0 and 00 and the remainging slots are numbered from 1 to 36 Find the probability that the ball lands in an odd numbered slot Your answer is

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ProbabilityThe answer above is NOT correct A basketball player makes 200 out of 220 free throws We would estimate the probability that the player makes the next free throw to be 0 91 Preview My Answers Submit Answers

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ProbabilityGovernment data assign a single cause for each death that occurs in the United States In a certain city the data show that the probability is 0 31 that a randomly chosen death was due to cardiovascular mainly heart disease and 0 15 that it was due to cancer a The probability that a death was due either to cardiovascular disease or to cancer is b The probability that the death was due to some other cause is

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ProbabilityThe data below was obtained from a random survey of 484 people The participants were asked their political party and whether they approve disapprove or have no opinion of how the president is doing his job The results of the survey are as follows 99 7 174 Democrat Republican Independent Total Approve 68 Disapprove 134 Undecided 28 Total 230 11 114 23 259 51 4 236 22 484 If a person if selected at random what is the empirical probability that the the person approves of the job the president is doing or is an independent

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ProbabilityOne card is drawn from a standard deck of 52 playing cards Find the probability of each of the following events 1 A spade is drawn 1 52 Answer 2 A seven is drawn 4 52 Answer 3 A spade or heart is drawn 5 52 Answer 4 A black jack is drawn 12 Answer 25 52

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ProbabilityA card is drawn randomly from a standard 52 card deck Find the probability of the given event a The card drawn is 4 The probability is b The card drawn is a face card The probability is c The card drawn is not a face card The probability is

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ProbabilityFour candidates are running for mayor The four candidates are Adams Brown Collins and Dalton Employing the subjective approach a political scientist has assigned the following probabilitites P Adams wins 0 55 P Brown wins 0 07 P Collins wins 0 27 P Dalton wins 0 11 Determine the probabilities of the following events Adams loses Either Brown or Dalton wins Either Adams Brown or Collins wins

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ProbabilityA survey asks adults to report their marital status Suppose that in the city which the survey is conducted 53 of adults are married 11 are single 25 are divorced and 11 are widowed Find the probabilities of each of the following events The adult is single The adult is not divorced The adult is either widowed or divorced

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ProbabilityAjar contains 6 white 10 blue and 13 red marbles If one marble is drawn at random from the jar find the probability that 1 the marble is white or blue Answer 2 the marble is white or red Answer 3 the marble is blue or red

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Probabilitya What is the probability that it is an ace b What is the probability that it is a heart

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ProbabilitySuppose that X is an event and that P X 0 29 What is P X i e the probability that X will not occur Answer

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ProbabilityComplete the following i Calculate the probability of the desired event rounded to 3 significant digits as needed ii Calculate the probability of the complementary event iii Compute the odds against and odds in favour of the event Rolling a number less than 3 on a 12 sided die

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ProbabilityWhat is the intermediate step in the form a a b as a result of completing the square fe he following equation 7x 65 11a 12

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Probabilityb If a participant is randomly selected from the study determine the probability that he she does not go to the gym for reasons not related to busyness or tiredness laziness P Other Round to 3 significant digits 0

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ProbabilityO Skewed left O Symmetric Skewed right Uniform 8 9 5 7 4 58 000111222344566788 6789

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ProbabilityCell phone user Not a cell phone user Total O 30 1000 O 490 500 O 10 500 Speeding violation 30 500 10 20 30 No speeding violation 490 480 970 Total Consider the table above Find the probability of selecting a person with speeding violation GIVEN that he she is a cell phone user 500 500 1000

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ProbabilitySuppose that three different closely related diseases A1 A2 and A3 occur in 25 15 and 12 of the population Find the probability of disease A2 given B3 using the table below O 0 44 O 0 23 0 30 0 28 Symptom State B B B B3 B4 no symptoms Disease State A A 08 18 06 68 A2 17 12 07 64 A3 10 14 08 68

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Probability80 O 86 O 86 5 22 86 5 O 87 Question 6 Consider the following dataset 77 79 80 86 87 87 94 99 Compute the range

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ProbabilitySuppose a quiz consist of 3 questions with 2 possible answer choices What is the probability that you get exactly 1 question correct 0 5 O 0 375 O 0 125 O 0 05

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ProbabilityThe accompanying display shows the average drive distance in yards for 199 professional golfers during a week on a tour in a recent year Complete parts a through d below Click the icon to view the display a Describe this distribution The distribution is and b Approximately what proportion of professional golfers drive on average 280 yards or less OA 90 B 75 C 20 O D 50 E 1 c Estimate the mean by examining the histogram Choose the correct answer below O A 270 yards B 300 yards C 280 yards D 310 yards OE 290 yards d Should the mean be expected to be smaller than approximately equal to or larger than the median Why Display of Goters 30 25 20 15 10 54 260 270 280 200 300 Average Drive Length yd Print Done 310 320 odu Q G 1

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ProbabilityThe average score on the Stats midterm was 80 points with a standard deviation of 6 points and Karl s z score was 1 How many points did he score He scored points

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Probability3 1 Terminology 66 1200 1000 800 600 400 200 D 1045 40 60 Total Figure 3 20 82 70 18 34 138 41 59 226 45 55 268 49 51 55 64 331 48 52 65 478 35 44 45 54 Sample Percent approve Percent disapprove 44 56 Male 567 37 63 Female 100 096 The graph in Figure 3 20 displays the sample sizes and percentages of people in different age and gender groups who were polled concerning their approval of Mayor Ford s actions in office The total number in the sample of all the age groups is 1 045 a Define three events in the graph 6 Describe in words what the entry 40 means c Describe in words the complement of the entry in the previous question A d Describe in words what the entry 30 means e Out of the males and females what percent are males f Out of the females what percent disapprove of Mayor Ford g Out of all the age groups what percent approve of Mayor Ford h Find P Approve Male i Out of the age groups what percent are more than 44 years old J Find P Approve Age 35

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Probability3 2 Independent and Mutually Exclusive Events Use the following information to answer the next 12 exercises The graph shown is based on more than 170 000 interviews that took place from January through December 2012 The sample consists of employed Americans 18 years of age or older The Health Index Scores are the sample space We randomly sample one type of Health Index Score the emotional well being score Occupation Service Transportation Manufacturing or production Sales Clerical or office Installation and repair Construction or mining Manager executive or official Business owner Nurse Professional Farming fishing or forestry Teacher K 12 Physician Figure 3 21 77 78 79 80 Health Index Score 81 82 83 84 85 68 Find the probability that a Health Index Score is 82 7 69 Find the probability that a Health Index Score is 81 0 70 Find the probability that a Health Index Score is more than 81 71 Find the probability that a Health Index Score is between 80 5 and 82 72 If we know a Health Index Score is 81 5 or more what is the probability that it is 82 7 73 What is the probability that a Health Index Score is 80 7 or 82 7 74 What is the probability that a Health Index Score is less than 80 2 given that it is already less than 81 75 What occupation has the highest Health Index Score 76 What occupation has the lowest emotional index score 77 What is the range of the data

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Probability31 Don t stop exercising An investigation of the effect of different levels of physical activity was conducted on identical male twins in Finland For each twin pair al though they had maintained the same activity level for most of their lives one twin had significantly reduced his or her activity over the last few years due to work or family pressures For each pair of twins body fat per centage endurance levels and insulin sensitivity were measured For the less active twin the results showed greater body fat worse endurance and levels of insulin sensitivity displaying early signs of metabolic disease 23 a What type of design is being used in this investiga tion Give the explanatory and response variables b Is this an experiment or an observational study Why c The article reports that the measurements were car

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Probability13 Healthy Diet and Cataracts The relationship between healthy diet and prevalence of cataracts was assessed using a sample of 1808 participants from the Women s Health Initiative Observational Study Having a high Healthy Eat ing Index score was the strongest predictor of a reduced risk of cataracts among modifiable behaviors considered The Healthy Eating Index score was created by the U S Department of Agriculture and measures how well a person s diet con forms to recommended healthy eating patterns The report concludes These data add to the body of evidence suggesting that eating foods rich in a variety of vitamins and minerals may contribute to postponing the occurrence of the most common type of cataract in the United States 12 a Explain why this is an observational study rather than an experiment b Although the result was statistically significant the authors did not use strong language in stating their conclusions instead using words such as suggesting and may Do you think that their language is appropriate given the nature of the study Why

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ProbabilityA hair salon surveyed 360 customers 100 females and 260 males to see if they are satisfied with the service The result is summarized in the following table Satisfied Not Satisfied Total Female 71 Male 219 Total 290 29 41 70 100 260 360 Type numbers in the boxes Part 1 10 points aby Part 2 10 points aby Part 3 10 points 30 points 1 If a customer is randomly selected from these 360 people the probability that he she is satisfied is Please round your answer to two decimal places 2 If we know the selected customer is a female then what is the probability that she is satisfied Please round your answer to two decimal positions P satisfied female 3 How about the probability that a randomly selected customer is a female if we know that the person is satisfied Please round your answer to two decimal positions

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ProbabilityThe following probabilities are based on data collected from U S adults Individuals are placed Type numbers in the boxes into a weight category based on weight height gender and age 10 points Underweight Healthy Weight Overweight not Obese Obese Probability 0 018 0 374 0 346 Your answer should be given to 3 decimal places 0 262 Based on this data what is the probability that a randomly selected U S adult weighs more than the healthy weight range

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ProbabilityThe probabilities for the amount that can be won on a lottery game are given in the table below Type numbers in the boxes Find the missing probability X 10 points Amount o 1 23 Probability 0 5 0 27 X 0 04 3 0 01

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ProbabilityTo plan for retirement Justin deposits 295 each quarter in an annuity that pays 7 interest compounded quarterly Payments will be made at the end of each quarter Find the total value of the annuity in 28 years Do not round any intermediate computations and round your final answer to the nearest cent If necessary refer to the list of financial formulas

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ProbabilityThe following data represents the GPA of a sample of 15 students enrolled in a history clas 3 4 3 9 4 0 2 8 3 5 2 6 3 2 3 6 1 9 2 1 2 0 3 3 2 4 1 8 3 2 a Find the first quartile Do not include the median in the calculations Answer b Find the third quartile Do not include the median in the calculations Answer c Find the mean Round to 2 decimal places

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ProbabilityData was collected for a sample of organic snacks The amount of sugar in mg in each snack is summarized in the histogram below Which statement best describes the meaning of one of the bars in the histogram Frequency 10 8 6 4 2 220 224 228 232 236 240 244 248 amount of sugar mg O246 snacks have 1 mg of sugar 1 snacks have about 246 mg of sugar O246 snacks have between 244 and 248 mg of sugar The largest number of snacks have 11 mg of sugar

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ProbabilityThe data in the figure below represents the number of stars earned by 140 performers in a talent competition Percentage of Performers N 140 35 30 25 20 15 0 1 2 3 Number of Stars 4 5 How many performers earned exactly 3 stars be careful compare the question wording to the scale on the

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ProbabilityGiven below are data that has approximately normal distribution data data data data 57 28 41 18 44 35 46 67 53 82 47 62 71 23 39 82 54 88 58 04 53 63 41 68 42 3 40 61 39 41 47 99 45 58 78 03 60 83 48 95 65 81 41 29 40 67 51 43 44 44 56 37 45 47 47 72 51 84 58 93 54 24 48 73 63 93 69 49 69 13 62 21 59 45 39 92 60 65 In building a grouped frequency distribution table for this data set how many values are there in the clas 64 99 Include the lower class limit but not the upper class limit

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ProbabilityFind the area under the standard O Answer Keypa Keyboard Shortc Normal Table to z Tables If you would like to look up the value in a table select the table you want to view then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key

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ProbabilityA small liberal arts college in the Northeast has 250 freshmen Sixty of the freshmen are education majors Suppose twenty five freshmen are randomly selected witho heplacement Step 1 of 2 Find the expected number of education majors in the sample Round your answer to two decimal places if necessary Answer Tables Keypa Keyboard Shortc

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ProbabilityA town recently dismissed 9 employees in order to meet their new budget reductions The town had 7 employees over 50 years of age and 18 under 50 If the dismissed employees were selected at random what is the probability that exactly 6 employees were over 50 Express your answer as a fraction or a decimal number rounded to four decimal places Answer ter your answer opens in new window Tables Keypad Keyboard Shortcuts

Statistics

ProbabilityThere are 8 black balls and 8 red balls in an urn If 4 balls are drawn without replacement what is the probability that exactly 1 black ball is drawn Express your answer as a fraction or a decimal number rounded to four decimal places Answer ndow Tables Keypad

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ProbabilityThere are 9 black balls and 6 red balls in an urn If 4 balls are drawn without replacement what is the probability that exactly 2 black balls are drawn Express your answer as a fraction or a decimal number rounded to four decimal places Answer llow to ont jour poor opens in new window Tables Keypad

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ProbabilityA certain insecticide kills 80 of all insects in laboratory experiments A sample of 6 insects is exposed to the insecticide in a particular experiment What is the probability that exactly one insect will die Round your answer to four decimal places Answer down Tables

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ProbabilityA certain insecticide kills 60 of all insects in laboratory experiments A sample of 7 insects is exposed to the insecticide in a particular experiment What is the probability that exactly 2 insects will survive Round your answer to four decimal places Answer Tables BEER

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ProbabilityAssume the random variable X has a binomial distribution with the given probability of obtaining a success Find the following probability given the number of trials and the probability of obtaining a success Round your answer to four decimal places P X3 n 4 p 0 8

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ProbabilityA researcher wishes to conduct a study of the color preferences of new car buyers Suppose that 50 of this population prefers the color red If 12 buyers are randoml selected what is the probability that exactly 2 buyers would prefer red Round your answer to four decimal places Answer How to enter your answer opens in new window Tables Keypad Keyboard Shortcu