Probability Questions and Answers

A standard pair of six sided dice is rolled What is the probability of rolling a sum less than 5 Express your answer as a fraction or a decimal number rounded to four decimal places

3 on the YRBS survey asked students what grade they were in Responses were coded as 1 9th grade 2 10th grade 3 11th grade 4 12th grade 5 other or no grade The codebook for the YRBS dataset can be viewed here a and create a pivot table using To answer the following questions download the YRBS dataset Q3 Remember to create a pivot table highlight the data you want in the table go to insert and click pivot table When the pivot table pops up you ll be given a menu of options to the right of your screen in Excel where you will need to click and drag Q3 to the rows box and click and drag Q3 to the values box You ll also want to change the value settings to count For a refresher on creating pivot tables view this YouTube tutorial Question 6 How many students in the sample were in 9th grade Question 7 What percent of students were in the 9th grade 3 pts 3 pts

improved in each group Did not improve Improved Unit 1 page 31c John Wiley Sons Inc All rights reserved Proportion 1 0 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 Verum Fake Conventional Acupuncture Acupuncture Treatment Treatment If you are unable to see the graph above you can download the image here O Verum acupuncture 52 Fake acupuncture 57 Conventional treatment 72 O Verum acupuncture 54 Fake acupuncture 56 Conventional treatment 3250 O Verum acupuncture 48 Fake acupuncture 43 Conventional treatment 28 O Verum acupuncture 50 Fake acupuncture 50 Conventional treatment 50

Frequency 12 10 90 2 90 100 10 Question 2 11 2 101 111 121 131 141 151 161 110 120 130 140 150 160 170 If you are unable to see the graph above you can download the image here 171 181 191 180 190 200 0 How many total people have a systolic blood pressure of 110 or less 201 210 0 211 220 3 pts

Listed below are pulse rates beats per minute from samples of adult males and females Find the mean and median for each of the two samples and then compare the two sets of results Does there appear to be a difference D Male 88 75 63 84 62 85 56 70 52 94 55 74 59 65 95 Female 81 78 92 85 73 66 95 63 93 67 79 92 75 70 76 Find the means The mean for males is beats per minute and the mean for females is beats per minute Type integers or decimals rounded to one decimal place as needed

While conducting double observer su Jade determine that Blake s detection probability was 0 8 Don t fret says Blake you ll get bet field experience as I have Let s inform

At the beginning of the year 1995 the population of Townsville was 3248 By the beginning of the year 2012 the population had reached 4922 Assume that the population is growing exponentially answer the followine A Estimate the population at the beginning of the year 2019 ROUND TO THE NEAREST PERSON The population at the beginning of 2019 will be about B How long from the beginning of 1995 will it take for the population to reach 9000 ROUND TO 2 DECIMAL PLACES The population will reach 9000 about years after the beginning of 1995 In what year will did the population reach 9000 e population will or did hit 9000 in the year

Statistics students participated in an experiment to test their ability to determine when 1 minute or 60 seconds had passed The results are given below in seconds 53 49 62 68 58 Compute the standard deviation to the nearest tenth of a second using the formula on the formula sheet The mean was calculated in Question 5 The standard deviation is

Testing What is meant by a p value Choose the correct answer bel OA The p value is the valu OB The p value is the prob

A quality analyst wants to construct a control chart for de machines all producing the same product are under contr particular quality variable Accordingly he sampled four un machine with the following results Machine 1 2 3 17 16 23 5 4 2 0 Measurements 422 15 25 15 17 18 25 23 22 What is the estimate of the sample average range based u

The Waves and the Wolves are evenly matched baseball teams When they play there is a 0 5 probability that the Waves will win If they play 15 times what is the probability that the Waves will win 10 of the games Round your answer to the nearest tenth of a percent A 4 2 B 15 3 C 19 6 D 9 2

2 The area of Norway is 24 more than the area of Colorado So Norway s of Colorado s area Hint Write out the formula that will area if produce this 24 then rearrange

Q 5 Three wires OA OB and OC support a package as shown If the maximum tension each wire can support is 0 5 kips determine the largest mass measured in slugs the wires can support in this configuration All dimensions are given in feet z x 8 6 W 7 5 5 B y

If P A 0 4 P B 0 5 and P A or B 0 8 then what is P A and B

Musical styles other than rock and pop are becoming more popular A survey of college students finds that 40 like country music 30 like gospel music and 10 like both What is the probability that a student likes gospel music if we know that he or she likes country music

Michael and Jack have lunch together They flip a coin to decide who pays for lunch and then flip a coin again to decide who pays the tip What is the probability that Jack will have to pay for lunch and the tip O 1 5 O 1 4 01 O 1 2 1 8

Suppose P A 0 7 and P B 0 4 Are events A and B mutually exclusive O No they are not mutually exclusive Not enough information to determine O Yes they are mutually exclusive

Rolling a single die 20 times and keeping track of the numbers 1 6 that are rolled Is the number following a binomial distribution If not state the reason why No there are more than two outcomes for each trial O No there are two many trials No the trials are not independent O Yes it follows a binomial distribution No its probability changes over trials

58013 20492 87901 91277 25729 48891 56549 36224 Starting at the beginning of the row what are the first 12 numbers between 01 and 99 in the sample 2 generate 12 random numbers between 01 and 99 3 4 5 6 7 17 8 9 10 11 12

17 Piper invests 880 in an account with 0 45 interest compounded continuously for 5 years John invested the same amount of money at an interest rate of 0 5 compounded monthly for 5 years Who made more money Show work

Consider randomly selecting a student at a large university and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard Suppose that P A 0 7 and P B 0 3 a Could it be the case that P A n B 0 5 Why or why not Hint For any two sets A and B if A is a subset of B then P A P B Yes this is possible Since B is contained in the event A n B it must be the case that P B P An B and 0 5 0 3 does not violate this requirement Yes this is possible Since A n B is contained in the event B it must be the case that P B P An B and 0 5 0 3 does not violate this requirement No this is not possible Since B is equal to An B it must be the case that P A n B P B However 0 5 0 3 violates this requirement No this is not possible Since A n B is contained in the event B it must be the case that P A n B P B However 0 5 0 3 violates this requirement No this is not possible Since B is contained in the event A n B it must be the case that P A n B P B However 0 5 0 3 violates this requirement b From now on suppose that P An B 0 2 What is the probability that the selected student has at least one of these two types of cards c What is the probability that the selected student has neither type of card d Describe in terms of A and B the event that the selected student has a Visa card but not a MasterCard AUB An B OA U B A n B Calculate the probability of this event P J B e Calculate the probability that the selected student has exactly one of the two types of cards S E O 20

The computers of six faculty members in a certain department are to be replaced Two of the faculty members have selected laptop machines and the other four have chosen desktop machines Suppose that only two of the setups can be done on a particular day and the two computers to be set up are randomly selected from the six implying 15 equally likely outcomes if the computers are numbered 1 2 6 then one outcome consists of computers 1 and 2 another consists of computers 1 and 3 and so on a What is the probability that both selected setups are for laptop computers Round your answer to three decimal places b What is the probability that both selected setups are desktop machines c What is the probability that at least one selected setup is for a desktop computer Round your answer to three decimal places d What is the probability that at least one computer of each type is chosen for setup Round your answer to three decimal places

Four universities 1 2 3 and 4 are participating in a holiday basketball tournament In the first round 1 will play 2 and 3 will play 4 Then the two winners will play for the championship and the two losers will also play One possible outcome can be denoted by 1324 1 beats 2 and 3 beats 4 in first round games and then 1 beats 3 and 2 beats 4 Enter your answers in set notation Enter EMPTY or for the empty set a List all outcomes in S S b Let A denote the event that 1 wins the tournament List outcomes in A A c Let B denote the event that 2 gets into the championship game List outcomes in B B d What are the outcomes in A U B AUB What are the outcomes in A n B An B What are the outcomes in A A

A mutual fund company offers its customers a variety of funds a money market fund three different bond funds short intermediate and long term two stock funds moderate and high risk and a balanced fund Among customers who own shares in just one fund the percentages of customers in the different funds are as follows Money market Short bond Intermediate bond Long bond 21 12 12 5 High risk stock Moderate risk stock Balanced S 19 S 25 A customer who owns shares in just one fund is randomly selected a What is the probability that the selected individual owns shares in the balanced fund 6 b What is the probability that the individual owns shares in a bond fund c What is the probability that the selected individual does not own shares in a stock fund

For each variable decide if it is categorical or numerical a Hair color O Numerical Categorical b Amount of candy handed out on Halloween O Categorical Numerical c Number of text messages on Tuesdays Numerical O Categorical d Employee number Numerical O Categorical e Bus arrival time Numerical O Categorical

a Determine the shape of the distribution pictured below and the measure of center that should be used Frequency 25 20 15 10 5 0 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 data Q O Uniform O Symmetric O Skewed right O Skewed left b Based on the shape of the histogram above what measure of center should be used O mean O median

You work for a large farm with many fields of corn You are investigating the mass of a sample of ears of corn You gather the following data Mass g of ears of corn 18 6 12 6 12 9 13 1 13 6 14 7 15 1 15 2 15 3 16 2 17 6 18 1 18 8 19 2 19 5 19 6 19 9 22 2 22 9 23 0 23 6 23 8 24 8 31 3 Some of the masses in the sample seem much larger than the rest so you want to test for outliers Here are your summary Statistics Mean St Dev 18 8 4 6 Min Q1 Med Q3 Max 12 6 15 15 18 7 22 55 31 3 Apply the 1 5 IQR rule to search for outliers Calculate the lower and upper fences to 3 decimal places a IQR b Lower Fence c Upper Fence d Are there any outliers by the 1 5 IQR rule Enter yes or no

Does this describe an observational study or an experiment The growth rate of bacteria is compared before and after adding alcohol O Observational Study O Experiment

You have a bag of marbles with 5 blue marbles 3 yellow marbles and 4 red marbles Find the following probability of drawing the given marbles from the bag if you draw them without replacement Round your answers to 4 decimal places a A blue then a red b A red then a yellow c A blue then a blue then a blue Question Help Message instructor

In a particular bag of skittles there are 11 red 9 orange 10 green 14 yellow and 11 purple skittles Give the indicated probability Enter your answer as a decimal to 4 decimal places a Selecting a yellow skittle b Selecting a red or a purple skittle c Not selecting a green skittle d Selecting two consecutive orange skittles if you draw twice with replacement

Use the multiplication principle to solve An auto manufacturer produces 7 models each available in 8 different colors with 5 different upholstery fabrics and 9 interior colors How many varieties of car are available The manufacturer can produce different varieties of car

The adult men of the Dinaric Alps have the highest average height of all regions The distribution of height is approximately normal with a mean height of 6 ft 1 in 73 inches and standard deviation of 3 inches 5 Find the 40th percentile of the height of Dinaric Alps distribution for men 2 20 6 What percentage of men have a height greater than 74 inches DTG 30 50 70 90

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Suppose that E and F are two events and that P E 0 2 and P FE 0 5 What is PE O F

a customer buys 10 light bulbs 30 if damage occurs specify A get exactly 5 good light bulbs B at least 4 good light bulbs 10 37 51 AM

21 The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 3 5 minutes and a standard deviation of 1 minute Find the probability that a randomly selected college student will take between 2 0 and 4 5 minutes to find a parking spot in the library lot A 0 7745 B 0 4938 C 0 2255 D 0 0919

There are 12 members on a city council At a recent city council meeting 4 of the council members voted in favor of a budget increase How many possible groups of council members could have voted in favor Will the calculation involve permutations or combinations combinations permutations There are possible groups of 4 city council members who voted in favor of the budget increase

A random sample of 241 students were asked what kind of vehicle they prefer a car or truck The following contingency table gives the two way classification of the responses Car Truck Male 58 70 Female 30 83 Suppose one student is randomly selected from the group Calculate the following probabilities Round solutions to three decimal places if necessary P Female P Car P Female Truck P Truck Female Are the events Female and Truck indpendent or dependent

A random sample of 419 students and professors were asked about their political party affiliation The following contingency table summarizes their responses Republican 54 73 Suppose one participant is randomly selected from the group Calculate the following probabilities Round solutions to three decimal places if necessary P Student and Independent Student Professor Independent 72 97 P Republican and Professor P Democrat or Professor P Democrat or Independent P Republican and Independent Democrat 58 65

According to the American Automobile Association AAA 8 4 of Americans plan to travel by car over the next holiday weekend and 89 1 plan to stay home What is the probability that a randomly selected American plans to stay home or travel by car over the next holiday weekend P travel by car or stay home This probability does not equal 1 because Select an answer

0 13C0 12Co 11Co Thus we expect that for any n in general Co 13C1 12C1 11C Thus we expect that for any n in general C 13C13 12C12 11C11 Thus we expect that for any n in O

There are 440 physicians practicing in Port St Lucie Of them 88 are female and 60 are dermatologists total Of the 88 female physicians 12 are dermatologists Suppose one physician from Port St Lucie is randomly selected Calculate the following probabilities and determine if Female and Dermatologist are independent or dependent events Also determine if the events Female and Dermatologist are mutually exclusive or mutually non exclusive Round solutions to three decimal places if necessary P female P female dermatologist Therefore the events Female and Dermatologist are Select an answer The events Female and Dermatologist are Select an answer

P A 0 47 Round solutions to three decimal places if necessary Determine if A and B are independent or dependent events A and B are Select an answer Determine P A and B P A and B Determine if A and B are mutually exclusive or mutually non exclusive events A and B are Select an answer Determine P A or B P A or B ion to address the prompts below P B 0 15 P BA 0 12 events events

The probability that a randomly selected IRSC student is an athlete is 0 19 The probability that a randomly selected IRSC student is a biology major is 0 17 The probability that a randomly selected IRSC student is a biology major and an athlete is 0 09 Calculate the following probabilities Round solutions to three decimal places if necessary Determine the probability that a randomly selected IRSC student is a biology major given the student is an athlete P biology major athlete Determine the probability that a randomly selected IRSC student is an athlete given the student is major P athlete biology major biology

In a class of 25 students 15 are dual enrolled and 10 are not dual enrolled Suppose two students are randomly selected from the class without replacement Calculate the following probabilities Round solutions to three decimal places if necessary P Both Students are Dual Enrolled P 1st Student is Dual Enrolled and the 2nd Student is Not

Find the value of each of the following expressions 8 13 13 8 13 7 13 7 13C7 8C7 13C8 13P7

44 44 A of 4 S N4 34 go go go Submit All Parts to a 44 A The probability that a Heart or Spade is selected is 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 4 of Clubs is selected is The probability that a number smaller than 10 counting the ace as a 1 is selected is

A 5 4 d 5 i 844 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 or a Diamond is selected is The probability that a face card or Heart is selected is The probability that the selected card is both a face card and a Diamond is

Let M be the event that a randomly selected IRSC student is male and P M 0 53 Round solutions to three decimal places if necessary What is the probability that a randomly selected IRSC student is female P F Suppose two IRSC students are selected at random and calculate the following probabilities P Both students are male P Both students are female P the first student is male and the second student is female

A random sample of 128 students were asked if they lived on campus or off campus The following contingency table gives the two way classification of the responses On Campus Off Campus 55 12 23 38 Suppose one student is randomly selected from the group Calculate the following probabilities Round solutions to three decimal places if necessary P Female and Off Campus Male Female P Male and On Campus P Off Campus or Male P On Campus or Female