Probability Questions and Answers

The television show Green s Anatomy has been successful for many years That show recently had a share of 18 meaning that among the TV sets in use 18 were tuned to Green s Anatomy Assume that an advertiser wants to verify that 18 share value by conducting its own survey and a pilot survey begins with 12 households that have TV sets in use at the time of a Green s Anatomy broadcast Round solutions to four decimal places if necessary Find the probability that none of the households are tuned to Green s Anatomy P none Find the probability that at least one household is tuned to Green s Anatomy P at least one Find the probability that at most one household is tuned to Green s Anatomy P at most one

A softball coach is creating the starting lineup of 3 batters for the next game How many different ways can batters be selected for the starting lineup if 12 players are on the softball team Should this exercise involve permutations combinations or the fundamental counting principal Permutations Fundamental Counting Principle Combinations How many different starting lineups are possible There are different possible starting batter lineups

According to a recent study 80 of adult smokers started smoking before 21 years old A random sample of 14 smokers age 21 years or older is selected and the number of smokers who started smoking before 21 is recorded Calculate the following probabilities Round solutions to four decimal places if necessary 1 The probability that at least 2 of them started smoking before 21 years of age is P x 2 2 The probability that at most 6 of them started smoking before 21 years of age is P x 6 3 The probability that exactly 3 of them started smoking before 21 years of age is P x 3

The table below gives approximate probabilities for scoring 0 1 2 3 or 4 runs in one inning of Major League Baseball Although it is possible to score more than 4 runs in one inning the probability is very small so it is ignored in this question H x P x 0 67 0 18 0 07 Round solutions to three decimal places if necessary Compute the sum of these probabilities P x Compute the mean number of runs per inning using this probability distribution 0 1 2 3 0 05 4 0 03 Compute the standard deviation of this probability distribution

Ajar contains 5 red marbles numbered 1 to 5 and 7 blue marbles numbered 1 to 7 Find the following probabilities Round solutions to three decimal places if necessary a A marble is chosen at random If you re told the marble is red what is the probability that it has the number 3 on it P 3 red b The first marble is replaced and another marble is chosen at random If you re told the marble has the number 1 on it what is the probability the marble is red P red 1 1

responses Pass Did Study 32 Did Not Study 36 Suppose one student is randomly selected from the group Calculate the following probabilities Round solutions to three decimal places if necessary P Did Study and Pass P Did Not Study and Fail P Pass or Did Not Study P Fail or Did Study P Fail and Pass P Pass or Fail owing contingency table gives the two way classification of their Fail 25 16

A recent Gallup Poll found that 94 of American adults are satisfied with their personal life Suppose you take a random sample of 5 Americans and ask each one if they are satisfied with their personal life and record the number who report personal life satisfaction Use this experiment to answer the following questions Round solutions to four decimal places if necessary a Create a binomial probability distribution table for this experiment P x X f 0 1 2 3 4 5 b Calculate the mean of the binomial distribution c Calcualte the standard deviation of this binomial distribution

Tracee buys a bag of cookies that contains 5 chocolate chip cookies 5 peanut butter cookies 9 sugar cookies and 5 oatmeal cookies What is the probability that Tracee randomly selects a chocolate chip cookie from the bag eats it then randomly selects a sugar cookie Round the solution to four decimal places if necessary P chocolate chip cookie first and sugar cookie second

The data from a recent test are organized by sex and letter grade Use this information to calculate the following probabilities Round solutions to three decimal places if necessary B C Total 6 9 7 16 5 Total 20 22 14 If one student is chosen at random Find the probability that the student got a B A Male 13 Female P got a B Find the probability that the student was male and got a A P male and A Find the probability that the student was female or got an B P female or B If one student is chosen at random find the probability that the student got a C given they are male 28 28 56 P male

At I Love Food restaurant you can choose from 8 appetizers 8 entrees and 2 desserts How many three course meals can you order There are possible three course meals

In a large school it was found that 60 of students are taking a math class 73 of student are taking an English class and 49 of students are taking both Find the probability that a randomly selected student is taking a math class or an English class Write your answer as a decimal and round to 2 decimal places if necessary P Math or English Find the probability that a randomly selected student is taking neither a math class nor an English class Write your answer as a decimal and round to 2 decimal places if necessary P Not Math nor English

There are 129 students in a large class Of them 43 are female and 14 are STEM majors total Of the 43 female students 7 are STEM majors Suppose one student is randomly selected Calculate the following probabilities and determine if Female and STEM major are independent or dependent events Also determine if the events Female and STEM major are mutually exclusive or mutually non exclusive Round solutions to three decimal places if necessary P female P female STEM major Therefore the events Female and STEM major are Select an answer The events Female and STEM maior are

A sample of 405 salmon in a hatchery are tested for a particular disease It is found that 27 of them test positive for the disease Round solutions to three decimal places if necessary The empirical probability that a randomly chosen salmon will test positive is P Test Positive The empirical probability that a randomly chosen salmon will test negative is P Test Negative

Six different dice are rolled and the nun Next possible Should this exercise involve permutations combinations or the fundamental counting principal Fundamental Counting Principle Combinations Permutations There are a total of showing are recorded How many different outcomes are Question Help Video possible outcomes when 6 dice are rolled

Determine whether or not the distribution is a discrete probability distribution and select the reason Answer x 4 24 1 3 P X x Decide 4 78 Reason First decide whether the distribution is a discrete probability distribution then select the reason for m Yes No 6 113 Since the probabilities lie inclusively between 0 and 1 and to 1 is greater than

Suppose that there are ten students in a classroom a What is the probability that two of them have the same birthday day and mont b How many students would need to be in the class for the probability that two o have the same birthday to be greater than 0 5

Mrs Burke s chemistry class has 115 students cla yesterday s work

Consider the following table Amount of Life Insurance on Wife thousands of

The following pair of variables has a high positive linear correlation Number of car accid s it reasonable to conclude that an increase in one variable causes an Answer D Both Number of car accidents and Number of emergency room patie Number of emergency room patients increases

To determine if these data provide convincing evidence that more than 25 of business travelers check baggage 100 simulated samples of 12 business travelers were selected assuming that 25 check baggage The dotplot shows the number of business travelers in each simulated sample that check baggage 0 3 8 Simulated sample count of business travelers that check baggage d Use the results of the simulation to estimate the probability that 6 or more of the 12 randomly selected business travelers check baggage e Based on the actual result of 6 business travelers that checked baggage and your answer to part d is there convincing evidence that more than 25 of business travelers check baggage Explain your reasoning

The figure shows three forces acting on a pin supported rectangular plate at points A B and C Use the scalar method of computing moments in this problem a Compute the moment of the force at A about D and write your answer in vector form note you can use the scalar method to find the moment b Compute the magnitude and orientation 0 0 180 of the smallest force Fg that creates the same moment about D that you found in part a c If FB 20 lb and 0 30 compute the magnitude of the horizontal force Fc that makes the resultant moment of these three forces about D equal to zero 16 in 30 in 23 55 lb A D 24 in B 20 in C FB Fc 0

Four students are trying to move a table from one corner of the classroom to another as illustrated in the figure top view The students hold the table from points A B C and E and apply pulling forces with magnitudes 20 N 35 N 5 N and 35 N respectively Compute the resultant moment in vector form of these four forces a About point A using the scalar method b About point D using the scalar method 20 N m B 35 N TE Elm 1 m 35 N 5 N 1 m

FR If 12 3 5 8 then y Estimate your answer to two decimal places 212

Sick computers Let be the event that a computer contains a virus and let W be the event that a computer contains a worm Suppose P V 0 12 P W 0 63 P V and W 0 04 4 points a Find the probability that the computer contains either a virus or a worm or both

There are 37 chocolates in a box all identically shaped There 11 are filled with nuts 12 with caramel and 14 are solid chocolate You randomly select one piece eat it and then select a second piece Find the probability of selecting 2 nut candies O A B C D 7 666 121 1369 55 666 110 1369 AU

A group of students were asked if they carry an ATM card The responses are listed in the table If a student is selected at random find the probability that he or she owns an ATM card given that the student is a freshman Round your answer to three decimal places Class ATM Card Carrier Not an ATM Card Carrier Freshman Sophomore Total OA 0 717 B 0 430 OC 0 283 43 21 64 17 19 36 Total 60 40 100

Find the indicated probability If necessary round to three decimal places Suppose that E and F are two events and that P E 0 6 and P FE 0 7 What is P E and F OA 0 042 OB 0 857 OC 1 300

Find the indicated probability Give your answer as a simplified fraction The manager of a used car lot took inventory of the automobiles on his lot and constructed the following table based on the age of his car and its make foreign or domestic A car was randomly selected from the lot Given that the car selected was a domestic car what is the probability that it was older than 2 years 0 2 3 5 6 10 over 10 Total Make Foreign Domestic Total OA 81 OB O C 81 200 59 100 41 40 41 81 30 22 52 13 10 23 17 724 44 100 100 200

Consider the data in the table shown which represents the marital status of males and females 18 years or older in the United States in 2003 Determine the probability that a randomly selected U S resident 18 years or older is divorced or a male Round to the nearest hundredth Never married Married Widowed Divorced Males in millions UA 0 50 B 0 58 OC 0 54 OD 0 04 28 6 62 1 2 7 9 0 Females in millions 23 3 62 8 11 3 12 7 110 1 Total in millions 51 9 124 9 14 0 21 7 212 5 Total in millions 102 4 Source U S Census Bureau Current Population reports 0

The sample space for tossing three fair coins is HHH HHT HTH HTT THH THT TTH TTT What is the probability of exactly two heads OA 3 1 2 OB OC 3 AFP

A psychic network received telephone calls last year from over 1 5 million people A recent article attempts to shed some light onto the credibility of the psychic network One of the psychic network s psychics agreed to take part in the following experiment Five different cards are shuffled and one is chosen at random The psychic will then try to identify which card was drawn without seeing it Assume that the experiment was repeated 50 times and that the results of any two experiments are independent of one another If we assume that the psychic is a fake i e they are merely guessing at the cards and have no psychic powers find the probability that they guess at least three correctly Round to six decimal places OA 0 004371 B 0 001093 O C 0 998715 D 0 001257 www

Eye color is an inherited trait For purposes of this problem assume that only two eye colors are possible brown and blue Use b to represent a blue eye gene and B a brown eye gene If any B genes are present the person will have brown eyes The table shows the four possibilities for the children of two Bb brown eyed parents where each parent has one of each eye color gene Find the probability that these parents give birth to a child who has blue eyes Second Parent O First Parent OA 2 OB 0 O c 1 B b B BB Bb b Bb bb

The red blood cell counts in 10 cells per microliter of a healthy adult measured on 5 days are as follows 51 52 50 49 53 Send data to calculator Find the standard deviation of this sample of counts Round your answer to two decimal places If necessary consult a list of formulas

A single 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 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 5 4 5 5 5 8 6 1 6 2 6 3 6 4 6 5 6 6 Find the probability of getting two numbers whose sum is greater than 10 OA B 1 18 D 1 12 O c 3 5 18

A die is rolled The set of equally likely outcomes is 1 2 3 4 5 6 Find the probability of getting a 7 OA 7 OB 1 7 09 6 OD O

31 Playing the horses In horse racing one can make a trifecta bet by specifying which horse will come in first which will come in second and which will come in third in the correct order One can make a box trifecta bet by specifying which three horses will come in first second and third without specifying the order a In an eight horse field how many different ways can one make a trifecta bet b In an eight horse field how many different ways can one make a box trifecta bet

In a sandwich shop the following probability distribution was obtained The random variable x represents the number of condiments used for a hamburger Find the mean and standard deviation for the random variable x Round to two decimal places X P x 0 0 30 1 0 40 2 0 20 30 06 4 0 04 A mean 1 30 standard deviation 1 54 B mean 1 30 standard deviation 2 38 C mean 1 14 standard deviation 1 04

A lab orders a shipment of 100 rats a week 52 weeks a year from a rat supplier for experiments that the lab conducts Prices for each weekly shipment of rats follow the distribution below Price 10 00 12 50 15 00 Probability 0 2 0 15 0 65 How much should the lab budget for next year s rat orders assuming this distribution does not change Round to the nearest cent Hint Find the expected price OA 3 664 200 00 B 13 63 OC 1 363 00 D 708 50

A quiz consists of 80 multiple choice questions each with five possible answers only one of which is correct If a student guesses on each question what is the mean and standard deviation of the number of correct answers Round to three decimal places OA mean 4 standard deviation 2 OB mean 16 standard deviation 1 265 OC mean 16 standard deviation 3 578 OD mean 4 standard deviation 3 578

A high school has 44 players on the football team The sur 154 150 160 170 170

A recent survey found that 62 of all adults over 50 wear sunglasses for driving In a random sample of 80 adults over 50 what is the mean and standard deviation of those that wear sunglasses Round to three decimal places OA mean 49 6 standard deviation 4 341 OB mean 49 6 standard deviation 2 227 OC mean 3 04 standard deviation 4 341 OD mean 3 04 standard deviation 2 227

In a recent survey 73 of the community favored building a health center in their neighborhood If 14 citizens are chosen find the probability that exactly 5 of them favor the building of the health center Round to the nearest three decimal places A 0 003 B 0 730 C 0 169 D 0 357

If p is the probability of success of a binomial experiment then what is the probability of failure OA 1 p B P OC P 2 D p 1 P www

The peak shopping time at a home improvement store is between 8 00am and 11 00am on Saturday mornings Management at the home improvement store randomly selected 155 customers last Saturday morning and decided observe their shopping habits They recorded the number of items that each of the customers purchased as well as total time the customers spent in the store Identify the types of variables recorded by the home improvement store A number of items discrete total time continuous B number of items continuous total time discrete C number of items continuous total time continuous D number of items discrete total time discrete

The following stem and leaf plot represents the times

1 A random sample of 200 patients is selected from a large medical clinic and each is classified as to whether or not they take an omega 3 fish oil tablet daily It was found that those who consumed an omega 3 tablet every day had lower average cholesterol levels than those who did not and that the difference is statistically significant Is this an experiment or an observational study Explain This is an experiment Here treatments response individuais there to measure Explain how confounding may impact the results of the study If the Variable from each response other Can the results of this study be generalized to all patients at the large medical clinic Yes Ves Can we conclude that taking an omega 3 fish oil tablet every day causes a reduction in cholesterol levels Explain your reasoning 1 Has everyday because couldn t be distinguished imposed after those cholesterol Found that had lower the ex pen ment took the

III Test Final Exam Study Guide Question list Question 1 Question 2 Question 3 Question 4 Question 5 K The following is a set of data from a sample of n 65 89 4 a Compute the mean median and mode b Compute the range variance standard deviatic c Compute the Z scores Are there any outliers d Describe the shape of the data set myvi v c Compute the Z scores Data X 6 5 8 9 4 Are there any outliers Z

a Calculate the probability of sampling at random a fish that is smaller in size than the value you would obtain by subtracting half the standard deviation from the average x will be equal to 0 2 b Calculate the probability of sampling at random a fish that is greater in size than the value you would obtain by adding half the standard deviation from the average x 0 2 c Calculate the probability of sampling at random a fish that has a size between the two values x 0 2 x 0 2 used in parts a and b respectively d Calculate the 25th and 75th percentiles of fish size for the population using the normal distribution table e Imagine that 5 individuals are sampled at random from this fish population Calculate the probability that the average calculated will be less than the value u 0 3 B2 1 23 st 4 LO 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 A 356 78 362 06 339 0281 362 82 364 65 355 67 336 29 312 84 299 98 310 86 308 97 325 33 319 5 322 14 339 01 334 6 356 32 350 58 336 34 338 32 361 53 365 B fx AVERAGE A1 A21 C Average D E F H Standard deviation

8 10 Points DETAILS Use the following matrix 0 2 1 3 1 0 2 A 3 1 Write the transpose of mat

6 10 Points DETAILS Find x y z and w X 59 6 yz w 64 11 059 677 764