Probability Questions and Answers

collect 600 Complete parts a through e 597 Type an integer or a decimal Do not round d Find the expected value for a 3 bet 2 4 Type an integer or a decimal Do not round e If you bet 3 on a certain casino game the expected value is 3 5c Which bet is better in the sense of producing a higher expected value a 3 bet on the state s lottery or a 3 bet on the casino game Explain OA Neither bet is better because both games have the same expected value OB The state s lottery is a better bet because it has a larger expected value OC The casino game is a better bet because it has a larger expected value OD It is impossible to compare the values because they have different units

Determine whether the given experiment results in a binomial experiment If not give the reason why not Rolling a single die 34 times keeping track of the number of 3s that are rolled Not binomial there is not a fixed number of trials Not binomial there are more than two outcomes for each trial Not binomial the trials are not independent O Not binomial for more than one of the reasons given in the above answer choices O This procedure results in a binomial distribution

5 What are the two key pieces of information we need to know about a correlation

There are 132 students in a large class Of them 44 are live off campus and 32 are economics majors total Of the 44 students who live off campus 8 are economics majors Suppose one student is randomly selected Calculate the following probabilities and determine if off campus and economics major are independent or dependent events Also determine if the events off campus and economics major are mutually exclusive or mutually non exclusive Round solutions to three decimal places if necessary P off campus P off campus economics major Therefore the events off campus and economics major are Select an answer The events off campus and economics major are Select an answer

Sabrina buys a bag of cookies that contains 4 chocolate chip cookies 5 peanut butter cookies 4 sugar cookies and 7 oatmeal cookies What is the probability that Sabrina randomly selects a sugar cookie from the bag eats it then randomly selects an oatmeal cookie Round the solution to four decimal places if necessary P sugar cookie first and oatmeal cookie second

Which of the following cannot be the probablity of an event 0 8 1 00 01 31 7 0 5 0 00 7

A certain drug is und to treat asthma Ianical trial of the drag 13 f 262 dbac xpand cher Chd on data from the manufacturer The

American Airlines flights from Fort Lauderdale to New York are on time 70 of the time Suppose 10 flights are randomly selected and the number on time flights is recorded Determine the following probabilities Round solutions to four decimal places if necessary The probability that exactly 8 flights are on time is P z 8 The probability that at most 7 flights are on time is P z 7 The probability that at least 4 flights are on time is DO

Suppose that probability that a randomly selected IRSC students is at least 19 years old is 0 55 Round solutions to three decimal places if necessary What is the probability that a randomly selected IRSC student is less than 19 years old P the student is less than 19 years old Suppose two IRSC students are selected at random and calculate the following probabilities P Both students are at least 19 years old P Both students are less than 19 years old P the first student is at least 19 years old and the second student is less than 19 years old

4 4 A A As shown above a classic deck of cards is made up of 52 cards Suppose one card is selected at random and calculate the following probabilities Round solutions to three decimal places if necessary The probability that a 6 of Diamonds is selected is The probability that a Spade or Diamond is selected is The probability that a number smaller than 4 counting the ace as a 1 is selected is

A boy owns 5 pairs of pants 5 shirts 5 ties and 5 jackets How many different outfits can he wear to school if he must wear one of each item He can wear different outfits

Given in the table are the BMI statistics for random samples of men and women Assume that the two samples are independent simple random samples selected from normally distributed populations and do not assume that the population standard deviations are equal Complete parts a and b below Use a 0 01 significance level for both parts a Test the claim that males and females have the same mean body mass index BMI What are the null and alternative hypotheses OA Ho H H H 4 OC Ho 2 H H1 H The test statistic t is Round to two decimal places as needed The P value is Round to three decimal places as needed State the conclusion for the test GEDEE b Construct a confidence interval suitable for testing the claim that males and fernales have the same mean BMI DH HL Round to three decimal places as needed Does the confidence interval support the conclusion of the test because the confidence interval contains OB Ho H H2 OD Ho H H H H H OA Reject the null hypothesis There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI OB Reject the null hypothesis There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI OC Fail to reject the null hypothesis There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI OD Fail to reject the null hypothesis There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI Male BMI Female BMI P 44 H n X 27 8884 s 8 242445 1 44 26 1997 4 670266

rite the equation 36 729 in logarithmic form

E and F are disjoint events then P E or F P E and F P F P E P F P E P F P E and F

Among 29 to 34 year olds 29 say they have called a talk show while under the influence of alcohol Suppose four 29 to 34 year olds are selected at random Complete parts a through d below a What is the probability that all four have called a talk show while under the influence of alcohol Round to four decimal places as needed b What is the probability that at least one has not called a talk show while under the influence of alcohol Round to four decimal places as needed c What is the probability that none of the four have called a talk show while under the influence of alcohol Round to four decimal places as needed d What is the probability that at least one has called a talk show while under the influence of alcohol Round to four decimal places as needed

Once a woman won 1 million in a scratch off game from a lottery Some years later she won 1 million in another scratch off game In the first game she beat odds of 1 in 4 2 million to win In the second she beat dds of 1 in 805 600 a What is the probability that an individual would win 1 million in both games if they bought one scratch off ticket from each game b What is the probability that an individual would win 1 million twice in the second scratch off game a The probability that an individual would win 1 million in both games if they bought one scratch off ticket from each game is Use scientific notation Use the multiplication symbol in the math palette as needed Round to the nearest tenth as needed b The probability that an individual would win 1 million twice in the second scratch off game is Use scientific notation Use the multiplication symbol in the math palette as needed Round to the nearest tenth as needed

point s possible ccording to a survey the probability that a randomly selected worker primarily drives a car to work is 0 751 The robability that a randomly selected worker primarily takes public transportation to work is 0 080 Complete parts a hrough d a What is the probability that a randomly selected worker primarily drives a car or takes public transportation to work worker drives a car or takes public transportation to work Type an integer or decimal rounded to three decimal places as needed b What is the probability that a randomly selected worker primarily neither drives a car nor takes public transportation work worker neither drives a car nor takes public transportation to work Type an integer or decimal rounded to three decimal places as needed c What is the probability that a randomly selected worker primarily does not drive a car to work P worker does not drive a car to work Type an integer or decimal rounded to three decimal places as needed d Can the probability that a randomly selected worker primarily walks to work equal 0 25 Why or why not OA Yes The probability a worker primarily drives walks or takes public transportation would equal 1 OB No The probability a worker primarily drives walks or takes public transportation would be greater than 1 O C No The probability a worker primarily drives walks or takes public transportation would be less than 1 Yon If owerk

How many different simple random samples of size 4 can be obtained from a population whose size is 51 The number of simple random samples which can be obtained is Type a whole number

Four members from a 33 person committee are to be selected randomly to serve as chairperson vice chairperson secretary and treasurer The first person selected is the chairperson the second the vice chairperson the third the secretary and the fourth the treasurer How many different leadership structures are possible There are possible different leadership structures Type an integer or fraction Simplify your answer

The distribution of Bachelor s degrees conferred by a university is listed in the table Assume that a student majors in only one subject What is the probability that a randomly selected student with a Bachelor s degree majored in Physics or Philosophy Round your answer to three decimal places OA 0 251 OB 0 527 OC 0 222 0 470 Major Frequency Physics Philosophy Engineering Business Chemistry 230 204 86 176 222

A club elects a president vice president and secretary treasurer How many sets of officers are possible if there are 12 members and any member can be elected to each position No person can hold more than one office OA 11 880 OB 660 OC 1 320 OD 440

The managers of a corporation were surveyed to determine the background that leads to a successful manager Each manager was rated as being either a good fair or poor manager by his her boss The manager s educational background was also noted The data appear below Given that a manager is only a fair manager what is the probability that this manager has no college background Give your answer as a simplified fraction H S Degree Some College College Degree Master s or Ph D Totals Good Fair Poor Totals OA O C 5 87 5 17 3 5 9 17 2 17 7 26 24 42 8 74 O B O D 1 32 99 160 10 2 13 23 10 39 87 34 43 160

n 5 card poker played with a standard 52 card deck 2 598 960 different hands are possible If there are 624 different ways a four of a kind can be dealt find the probability of not being dealt a four of a kind Express the probability as a Fraction but do not simplify 625 OA 2 598 960 624 OB 2 598 960 O C OD 2 598 336 2 598 960 1248 2 598 960

The table to the right represents a random sample of the number of deaths per 100 cases for a certain illness over time If a person infected with this illness is randomly selected from all infected people find the probability that the person dies 3 4 years after diagnosis Express your answer as a simplified fraction and as a decimal OA 1 35 O C 7 0 029 0 538 13 B 7 D 20 7 120 Years after Diagnosis Number of deaths 15 35 0 35 0 058 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 9 6 4 2 13

The age distribution of members of a gymnastics association is shown in the table A member of the association is selected at random Find the probability that the person selected is between 26 and 35 inclusive Round your answer to three decimal places OA 0 047 OB 251 OC 0 231 D 0184 Age years Under 21 21 25 26 30 31 35 Over 35 Total Frequency 412 400 200 51 25 1 088

If a fair coin is tossed 10 times what is the probability of getting all heads Express the probability as a simplified fraction 1 OA 512 1 OB O C O D 1 1024 1 2048

single 6 sided die is rolled twice The set of 36 equally likely outcomes is 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6 Find the probability of getting two numbers whose sum is greater an 10 A 3 OB O C 1 12 5 18

Use the given data to complete parts a and b below 12 b Draw a scatter diagram of the data with the additional data point 10 4 9 3 Choose the correct answer below O A O B O C O D Ay Ay 8 4 X 2 2 4 4 1 5 3 3 6 4 7 4 9 04 yo 4 8 12 Q N AY 12 8 0 0 4 3 8 12 Q N Ay 12 8 0 C 4 x 8 12 Q O 12 8 0 4 8 12 Compute the linear correlation coefficient with the additional data point The linear correlation coefficient for the

A random sample of 1018 adults in a certain large country was asked Do you pretty much think televisions are a necessity or a luxury you could do without Of the 1018 adults surveyed 527 indicated that televisions are a luxury they could do without Complete parts a through e below Click here to view the standard normal distribution table page 1 Click here to view the standard normal distribution table page 2 a Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without p 0 518 Round to three decimal places as needed b Verify that the requirements for constructing a confidence interval about p are satisfied is stated to be The sample sample size 10 and the Round to three decimal places as needed a simple random sample the value of np 1 p is 254 182 which is greater than or equal to can be assumed to be less than or equal to 5 of the population size c Construct and interpret a 95 confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without Select the correct choice below and fill in any answer boxes within your choice Type integers or decimals rounded to three decimal places as needed Use ascending order OA There is a between OB We are probability the proportion of adults in the country who believe that televisions are a luxury they could do without is and confident the proportion of adults in the country who believe that televisions are a luxury they could do without is m

A television sports commentator wants to estimate the proportion of citizens who follow professional football Complete parts a through c Click here to view the standard normal distribution table page 1 Click here to view the standard normal distribution table page 2 a What sample size should be obtained if he wants to be within 4 percentage points with 96 confidence if he uses an estimate of 48 obtained from a poll The sample size is 656 Round up to the nearest integer b What sample size should be obtained if he wants to be within 4 percentage points with 96 confidence if he does not use any prior estimates The sample size is Round up to the nearest integer

A binomial experiment is performed a fixed number of times What is each repetition of the experiment called Choose the correct answer below OA Each repetition of the experiment is called a binomial random variable OB Each repetition of the experiment is called a success O c Each repetition of the experiment is called a trial OD Each repetition of the experiment is called a mean

What is the formula for the expected number of successes in a binomial experiment with n trials and probability o success p Choose the correct forumla below OA E X p OB E X 1 P 1 p OC E X np 1 P OD E X np

Suppose a life insurance company sells a 220 000 one year term life insurance policy to a 23 year old female for 220 The probability that the female survives the year is 0 999536 Compute and interpret the expected value of this policy to the insurance company The expected value is 117 92 Round to two decimal places as needed Which of the following interpretation of the expected value is correct OA The insurance company expects to make an average profit of 117 92 on every 23 year old female it insures for 1 year OB The insurance company expects to make an average profit of 10 72 on every 23 year old female it insures for 1 month OC The insurance company expects to make an average profit of 219 90 on every 23 year old female it insures for 1 year OD The insurance company expects to make an average profit of 19 99 on every 23 year old female it insures for 1 month

man is planning for college and takes a standardized test While registering for the test he is allowed to select three chools to which his scores will be sent at no cost If there are 13 colleges he is considering how many different ways ould he fill out the score report form e could fill out the score report form in different ways

In a survey of 400 randomly selected people it was determined that 22 play soccer What is the probability that a randomly selected person plays soccer The probability that a randomly selected person plays soccer is Type an integer or a decimal

Let sample space S 1 2 3 4 5 6 7 8 Suppose the outcomes are equally likely Compute the probability of the event E an odd number P E Type an integer or decimal rounded to three decimal places as needed

If a new car has 2 transmission types 3 vehicle styles 2 option packages 8 exterior color choices and 3 interior color choices how many different new cars are possible There are possible different cars DE

Find the probability P E or F if E and F are mutually exclusive P E 0 41 and P F 0 47 The probability P E or F is Simplify your answer

Let sample space S 1 2 3 4 5 6 7 8 9 10 Suppose the outcomes are equally likely Compute the probabilit the event E 3 5 9 P E Type an integer or decimal rounded to three decimal places as needed

Suppose that two cards are randomly selected from a standard 52 card deck a What is the probability that the first card is a queen and the second card is a queen if the sampling is done without replacement b What is the probability that the first card is a queen and the second card is a queen if the sampling is done with replacement D a If the sampling is done without replacement the probability that the first card is a queen and the second card is a queen is 0 005 Round to three decimal places as needed b If the sampling is done with replacement the probability that the first card is a queen and the second card is a queen Round to three decimal places as needed is

A bag of 27 tulip bulbs contains 12 red tulip bulbs 9 yellow tulip bulbs and 6 purple tulip bulbs Suppose two tulip bulb are randomly selected without replacement from the bag a What is the probability that the two randomly selected tulip bulbs are both red b What is the probability that the first bulb selected is red and the second yellow c What is the probability that the first bulb selected is yellow and the second red d What is the probability that one bulb is red and the other yellow a The probability that both bulbs are red is 0 188 Round to three decimal places as needed b The probability that the first bulb is red and the second is yellow is 0 154 Round to three decimal places as needed c The probability that the first bulb is yellow and the second is red is 0 154 Round to three decimal places as needed d The probability that one bulb is red and one is yellow is Round to three decimal places as needed

For the month of October in a certain city 39 of the days are cloudy Also in the month of October in the same city 29 of the days are cloudy and rainy What is the probability that a randomly selected day in October will be rainy if it is cloudy The probability is approximately Round to three decimal places as needed

This past semester a professor had a small business calculus section The students in the class were Jim Mike Kristin Al Pam Neta Allison Dave Jinita and William Suppose the professor randomly selects two peopl to go to the board to work problems What is the probability that Pam is the first person chosen to go to the board and Kristin is the second P Pam is chosen first and Kristin is second Type an integer or a simplified fraction

Suppose that a single card is selected from a standard 52 card deck What is the probability that the card drawn is a club Now suppose that a single card is drawn from a standard 52 card deck but it is told that the card is black What is the probability that the card drawn is a club The probability that the card drawn from a standard 52 card deck is a club is Round to three decimal places as needed

P A 0 42 P B 0 58 a Can you compute P A and B if you only know P A and P B Yes O No b Assuming that events A and B arise from independent random processes answer the following 1 What is P A and B ii What is P A or B Enter a number iii What is P A B 0 42 c If we are given that P A and B 0 19 are the random variables giving rise to events A and B independent Yes O No d If we are given that P A and B 0 19 what is P AIB Round your answer to four decimal places

4 A greenhouse in a tri county area has kept track of its customers for the last several years and has determined that 28 of its customers plant a vegetable garden in the spring The greenhouse obtains a random sample of 1000 of its customers a What is the mean and standard deviation of the sampling distribution of p the sample proportion of customers that plant a vegetable garden in the spring b What is the probability that more than 30 of its customers plant a vegetable garden in the spring Draw and label a curve and then give your answer c What is the probability that between 25 and 32 of its customers plant a vegetable garden in the spring Draw and label a curve and then give your answer

2 A physical fitness association is including the mile run in its secondary school fitness test The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 480 seconds and a standard deviation of 35 seconds a Find the probability that a randomly selected boy in secondary school can run the mile in less than 400 seconds Draw and label the curve and then answer the question Then give the percentage application of your answer b Find the probability that a randomly selected boy in secondary school will take more than 510 seconds for the run Draw and label the curve and then answer the question Then give the percentage application of your answer

Question 1 of b 1 Construct a 95 confidence interval for p p given the following summary statistics of two independent random samples P 0 54 p 0 48 n 200 and n 225 What is the left endpoint of the confidence interval Round your answer to the nearest thousandths Answer

In a particular survey of internet users 3517 respondents say that they use social networking sites and 1332 respondents say that they do not use social networking sites What is the probability that a randomly selected person uses a social networking site Does that result suggest that it is likely with a probability of 0 5 or greater for someone to use social networking sites The probability that a randomly selected person uses a social networking site is Round to three decimal places as needed

In a survey of U S adults with a sample size of 2040 362 said Franklin Roosevelt was the best president since World War II Two U S adults are selected at random from this sample without repl Complete parts a through d a Find the probability that both adults say Franklin Roosevelt was the best president since World War II The probability that both adults say Franklin Roosevelt was the best president since World War II is Round to three decimal places as needed b Find the probability that neither adult says Franklin Roosevelt was the best president since World War II The probability that neither adult says Franklin Roosevelt was the best president since World War II is Round to three decimal places as needed c Find the probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II The probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II is Round to three decimal places as needed d Which of the events can be considered unusual Explain Select all that apply None of these events are unusual The event in part c is unusual because its probability is less than or equal to 0 05 The event in part a is unusual because its probability is less than or equal to 0 05 The event in part b is unusual because its probability is less than or equal to 0 05