Probability Questions and Answers

Researchers watched dolphin groups off the coast of Ireland in 1998 to determine what activities the dolphin groups partake in at certain times of the day The numbers in table below represent the number of dolphin groups that were partaking in an activity at certain times of days Activity Morning Travel Feed Social Total 6 28 38 72 Noon 6 4 5 15 Afternoon 14 0 9 23 Evening 13 56 10 79 Total 39 88 62 189 a What is the probability that a dolphin group is partaking in travel Round your final answer to 3 decimal places b What is the probability that a dolphin group is around at noon Round your final answer to 3 decimal places c What is the probability that a dolphin group is partaking in travel given that it is around at noon Round your final answer to 3 decimal places d What is the probability that a dolphin group is around at noon given that it is partaking in travel Round your final answer to 3 decimal places e What is the probability that a dolphin group is around in the afternoon given that it is partaking in travel Round your final answer to 3 decimal places

Are the events wearing a sweatshirt and failing your statistics exam independent events Why or why not OYes because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event O No because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event No because they both cannot happen at the same time O Yes because they can both happen at the same time O Yes because they both cannot happen at the same time O No because they can both happen at the same time Yes because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event O No because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event

An experiment is rolling two fair dice a What is the probability that the sum is 8 Round answer to 3 decimal places b What is the probability that the sum is 8 given that the first die is a 3 Round answer to 3 decimal places c What is the probability that the first die is a 3 given that the sum is 8 Round answer to 3 decimal places d Are the events the sum is 8 and the first die is a 3 independent events Why or why not Round answer to 3 decimal places Select an answer e What is the probability that the sum is 7 Round answ to 3 decimal places f What is the probability that the sum is 7 given that the first die is a 4 Round answer to 3 decimal places g What is the probability that the first die is a 4 given that the sum is 7 Round answer to 3 decimal places

Are the events being a teenager and being in a car accident independent events Why or why not O No because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event O Yes because they both cannot happen at the same time O No because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event O Yes because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event O Yes because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event O No because they can both happen at the same time O No because they both cannot happen at the same time OYes because they can both happen at the same time

The number of people who survived the Titanic based on class and gender is in the following table Suppose a person is picked at random from the survivors Class 1st 2nd 3rd Total Female Male Total 135 60 195 94 24 118 79 59 138 308 143 451 a What is the probability that a survivor was female Round final answer to 3 decimal places b What is the probability that a survivor was in the 3rd class Round final answer to 3 decimal places c What is the probability that a survivor was a female given that the person was in 3rd class Round final answer to 3 decimal places I d What is the probability that a survivor was a female and in the 3rd class Round final answer to 3 decimal places e What is the probability that a survivor was a female or in the 3rd class Round final answer to 3 decimal places

Are the events clouds in the sky and raining independent events Why or why not Yes because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event No because they both cannot happen at the same time OYes because they can both happen at the same time No because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event Yes because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event No because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event O No because they can both happen at the same time Yes because they both cannot happen at the same time

Are the events passing your physics class and passing your calculus class independent events Why or why not O No because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event O No because they both cannot happen at the same time O Yes because they both cannot happen at the same time Yes because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event O No because they can both happen at the same time O No because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event Yes because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event Yes because they can both happen at the same time

Express the following probability as a simplified fraction and as a decimal If one person is selected from the population described in the table find the probability that the person is divorced given that this person is female Marital Status of a Certain Population Ages 18 or Older in Millions Married Divorced Widowed Total 64 66 130 Male Female Total Express the probability as a simplified fraction The probability is Type an integer or a simplified fraction Never Married 44 29 73 7 17 24 4 5 9 119 117 236

8 6 2y 3 y 4 y ne proportion for y

a Given A B C D 2 7 n 3 8 7n 3 16 Given 2n 3 56 2n 6 16 7n 21 16 b Solve the given equation Write your answer as an improper fraction in simplest n 9 7 5 2

21 Charlie bought a pair of shorts at the store when they were having a 45 off sale If the regular price of the pair of shorts was 24 how much did Charlie pay Answer

A television that normally sells for 459 is on sale at a 30 discount What is the sale price of the television 420 B 137 70 321 30 D 596 30

14 Solve for the value of z 5 SHOW HINT 25

a b Consider the two ratios 1 4 and 10 20 Are these two ratios equivalent Yes B No SHOW HINT Part B If the ratios 2 2 and 4 10 are equivalent then the value of a is

12 Use the picture to create a ratio between the objects LLLLLLLL The ratio of the number of footballs to the number of baseballs is the ratio of the number of baseballs to the number of footballs is

Choose the pairs of ratios below that represent equivalent rates Select all that app 1 10 20 3 B D 2 1 4 3 and and and and 6 5 16 9 20

Water Drain Water is draining from a tank connected to two pipes The speed f in feet per second at which water drains through the first pipe can be modeled by the function below where x is the depth of the water in the tank f x 64 x 2 Speed of water drainage in feet sec Depth of the water in the tank feel 1 What is the domain for this function Interpret the domain in context 2 Describe the end behavior for this function What does it mean for this scenario Mini Lesson

A normal distribution has a mean of 98 and a standard deviation of 6 Find the z score for a data value of 103 Round to twe

Suppose that the blood cholesterol levels of all men age 20 to 34 years follows the Normal distribution with mean H 188 milligrams per deciliter mg dl and standard deviation o 41 mg dl Macmillan Learning Choose an SRS of 1000 men from this population What is the sampling distribution of x ON 5 9451 mg dl 1 2965 mg dl ON 188 mg dl 41 mg dl ON 188 mg dl 4 1 mg dl ON 188 mg dl 1 2965 mg dl Now what is the probability that x falls within 3 mg dl of Give your answer to four decimal places P 185 191

41686 6 Suppose an individual is randomly selected from the population of all adult males living in the United States Let A be the event that the selected individual is over 6 ft in height and let B be the event that the selected individ ual is a professional basketball player Which do you think is larger P A B or P B A Why

52 A system consists of two identical pumps 1 and 2 If one pump fails the system will still operate However because of the added strain the remaining pump is now more likely to fail than was originally the case That is r P 2 fails 1 fails P 2 fails q If at least one pump fails by the end of the pump design life in 7 of all systems and both pumps fail during that period in only 1 what is the probability that pump 1 will fail during the pump design life

56 For any events A and B with P B 0 show that P A B P A B 1

Computer keyboard failures can be attributed to electri cal defects or mechanical defects A repair facility cur rently has 25 failed keyboards 6 of which have electrical defects and 19 of which have mechanical defects a How many ways are there to randomly select 5 of these keyboards for a thorough inspection without regard to order b c In how many ways can a sample of 5 keyboards be selected so that exactly two have an electrical defect If a sample of 5 keyboards is randomly selected what is the probability that at least 4 of these will have a mechanical defect

5 A sonnet is a 14 line poem in which certain rhyming patterns are followed The writer Raymond Queneau published a book containing just 10 sonnets each on a different page However these were structured such that other sonnets could be created as follows the first line of a sonnet could come from the first line on any of the 10 pages the second line could come from the second line on any of the 10 pages and so on successive lines were perforated for this purpose a How many sonnets can be created from the 10 in the book b If one of the sonnets counted in part a is selected at random what is the probability that none of its lines came from either the first or the last sonnet in the book

1 Each of a sample of four home mortgages is classified as fixed rate F or variable rate V a What are the 16 outcomes in b Which outcomes are in the event that exactly three of the selected mortgages are fixed rate c Which outcomes are in the event that all four mort gages are of the same type d Which outcomes are in the event that at most one of the four is a variable rate mortgage e What is the union of the events in parts c and d and what is the intersection of these two events f What are the union and intersection of the two events in parts b and c

16 An individual is presented with three different glasses of cola labeled C D and P He is asked to taste all three and then list them in order of preference Suppose the same cola has actually been put into all three glasses a What are the simple events in this ranking experiment and what probability would you assign to each one What is the probability that C is ranked first c What is the probability that Cis ranked first and Dis ranked last b

4 Suppose that 55 of all adults regularly consume coffee 45 regularly consume carbonated soda and 70 regu larly consume at least one of these two products a What is the probability that a randomly selected adult regularly consumes both coffee and soda b What is the probability that a randomly selected adult doesn t regularly consume at least one of these two products

Use Venn diagrams to verify the following two relationships for any events A and B these are called De Morgan s laws a AUB A B b ANB A UB Hint In each part draw a diagram corresponding to the left side and another corresponding to the right side

6 A college library has five copies of a certain text on reserve Two copies 1 and 2 are first printings and the other three 3 4 and 5 are second printings A student examines these books in random order stopping only when a second printing has been selected One possible outcome is 5 and another is 213 a List the outcomes in f b Let A denote the event that exactly one book must be examined What outcomes are in A c Let B be the event that book 5 is the one selected What outcomes are in B d Let C be the event that book I is not examined What outcomes are in C

Suppose that cars arrive Wendy s drive through at the rate of 40 cars per hour between noon and 1 00 p m A random sample of 40 one hour time periods between noon and 1 00 p m is selected and 44 1 is the mean number of cars arriving for this sample a Why is the sampling distribution of the sample mean x approximately normal What is the mean and standard deviation of the sampling distribution of x assuming that 40 and 40 b c What is the probability that a simple random sample of 40 one hour time periods results in a mean of at least 44 1 cars Is this result unusual What might we conclude

A company has a policy of retiring company cars this policy looks at number of miles driven purpose of trips style of car and other features The distribution of the number of months in service for the fleet of cars is bell shaped and has a mean of 41 months and a standard deviation of 4 months Using the 68 95 99 7 Empirical Rule what is the approximate percentage of cars that remain in service between 45 and 53 months The approximate percentage of cars that remain in service between 45 and 53 months is not enter the percent symbol Do

Find the values of the variables that make the quadrilateral a parallelogram 10a 17 B D D A 266 13 7a 7 206 17 b flc

What are the values of b and c S b C Submit R w 60

10 in 6 in b What is the length of the missing leg If necessary round to the nearest tenth inches

Suppose X is a random variable representing a pumps water pressure in pounds per square inch psi The random variable X is normally distributed with mean 120 psi and standard deviation 3 psi Part a 5 points What is the probability that water pressure is less than 115 5 psi or more than 124 5

Two packages ordered from Amazon will each arrive on either Wednesday Thursday or Friday Suppose the two packages arrive independently of one another and that for each the probabilities of amiving on each day are given in the following table Day Wednesday W Thursday T Friday F Probability 0 2 0 55 0 25 The following questions pertain to the random experiment that consists of observing the arrival days of each of the two packages Part a 5 points Identify the sample space for this random experiment Hint consider the permutation of the arrival days of two packages Parth 5 points Compute the probability of each outcome in the sample space using the

1 1 3

The joint pdf of X and Y is given by 6 xy f x y x 2 0 x 1 0 y 2 Part a 5 points Find the marginal pdf f y and the conditional pdf f y x

The accompanying data represent the monthly rate of return of a certain company s common stock for the past few years Complete parts a and b below Click the icon to view the data table a Determine and interpret the quartiles The first quartile is Q Round to four decimal places as needed The second quartile is Q Round to four decimal places as needed The third quartile is Q3 Round to four decimal places as needed Interpret the quartiles Choose the correct answer below OA Of the monthly returns 25 are less than or equal to the first quartile 50 are less than or equal to the second quartile and 75 are less than or equal to the third quartile OB The first quartile is the lower bound of plausible monthly returns and the third quartile is the upper bound plausible monthly returns Any monthly returns outside of these bounds are outliers The second quartile represents the most common monthly return OC The first quartile is one standard deviation below the mean or average monthly return the second quam is the mean and the third quartile is one standard deviation above the mean O D All monthly returns within one standard deviation of the mean are contained in the first quartile all mon returns within two standard deviations of the mean are contained in the second quartile and all monthl returns within three standard deviations of the mean are contained in the third quartile b Check the data set for outliers Select the correct choice below and if necessary fill in the answer box to your choice OA The outlier s is are Type an integer or a decimal Do not round Use a comma to separate answers as needed are no outliers in the data set

A sample of 20 registered voters was surveyed in which the respondents were asked Do you think Chang Johnson Ohm or Smith is most qualified to be a senator The results of the survey are shown in the table Chang Johnson Ohm Ohm Smith Johnson Ohm Chang Johnson Johnson Johnson Chang Chang Complete parts a and b to the right Chang Smith Johnson Ohm Smith Chang Chang a Determine the mode candidate O Ohm O Johnson O Chang O Smith b Do you think it would be a good idea to rotate the candidate choices in the question Why OA Yes to avoid response bias OB Yes to make the resulting counts all closer to each other C Yes to confuse the respondents

Researchers wanted to determine if there was an association between the level of satisfaction of an individual and their risk of lung cancer The researchers studied 1613 people over the course of 5 years During this 5 year period they interviewed the individuals and asked questions about their daily lives and the hassles they face In addition hypothetical scenarios were presented to determine how each individual would handle the situation These interviews were videotaped and studied to assess the emotions of the individuals The researchers also determined which individuals in the study experienced any type of lung cancer over the 5 year period After their analysis the researchers concluded that the satisfied individuals were less likely to experience lung cancer Complete parts a through c a What type of observational study was this Explain This was a because information was collected about a group of individuals b What is the response variable What is the explanatory variable The response variable is The explanatory variable is because it because it c In the report the researchers stated that the research team also hasn t ruled out that a common factor like genetics could be causing both the emotions and the lung cancer Explain what this sentence means Choose the correct answer below OA The researchers may be concerned with confounding that occurs when the effects of two or more explanatory variables are not separated or when there are some explanatory variables that were not considered in a study but that affect the value of the response variable OB The researchers thought that genetics had greater influence than level of satisfaction OC It is not important to adjust for explanatory variables

A player is dealt 3 cards from a standard 52 card deck Determine the probability of being dealt two of a kind such as two aces or two kings by answering questions a through d a How many ways can 3 cards be selected from a 52 card deck There are ways that 3cards can be selected from a 52 card deck Type a whole number b Each deck contains 4 twos 4 threes and so on How many ways can two of the same card be selected from the deck ways that two of the same card can be selected from the deck There are Type a whole number c The remaining card must be different from the 2 chosen After selecting the two of a kind there are 12 different ranks of cards remaining in the deck that can be chosen Of the 12 ranks remaining the player chooses 1 of them and then selects one of the 4 cards in the chosen rank How many ways can the player select the remaining card There are ways the player can select the remaining card Type a whole number d Use the General Multiplication Rule to compute the probability of obtaining two of a kind That is what is the probability of selecting two of a kind and one card that is different The probability of obtaining two of a kind from 3 cards dealt is Round to four decimal places as needed

Suppose the commuter trains of a public transit system have a waiting time of up to fourteen minutes during peak rush hour periods Assume the waiting times in this interval follow a uniform distribution between 0 and 14 minutes It may be helpful to draw a sketch a Find the probability of waiting between two and seven minutes Round to four decimal places if necessary P 2 X 7 b Find the probability of waiting exactly five minutes Round to four decimal places if necessary P X 5

The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore seat belt Driver Survived Driver Died Total The probability as a decimal is Round to three decimal places as needed Wore Seat No Seat Belt Belt 411 455 The probability as a fraction is Tyne an integer or a simplified fraction 166 330 Total 510 1693 2203 411 965 168 023 579 988 Find the probability of not surviving a car accident given that the driver wore a seat belt 577 785

The time it takes a person to wash the dishes is uniformly distributed between 5 minutes and 13 minutes What is the probability that a randomly selected event of washing dishes will take a person between 8 and 12 minutes Round your answer accurate to two decimal places

The uniform distribution of a random variable X is given in the figure below 0 1 X 2 From the figure what is the probability that a randomly selected X is between 0 86 and 1 44 Round you answer to two decimal places

Suppose this distribution represents the probabilities of extending our class a minutes past the end of class time 0 20 0 1 2 The variable is continuous 3 4 5 because there exist fractional amounts of time The total area of the distribution rectangle is and the sum of all the probabilities should be 1 which makes sense as it is a probability distribution The probability in decimal form of the class extending 3 or more minutes beyond the end time is found by determining the area to the right of a 3 or the complement of the area to the left The probability in decimal form of the class extending 3 or less minutes beyond the end time is found by determining the area to the left of x 3 Remember that when we read our distribution tables for many of our distributions the area quoted in the tables is to the left so it is important to be able to recognize the need for using the complement to find the area to the right

2 ints Express the following comparative income statements in common size percents Using the common size percents which item is most responsible for the decline in net income Complete this question by entering your answers in the tabs below Income Statement Reason for Decline in Net Income Express the following comparative income statements in common size percents Note Round your percentage answers to 1 decimal place Sales Cost of goods sold Gross profit Operating expenses Net income GOMEZ CORPORATION Comparative Income Statements For Years Ended December 31 Current Year Current Year Answer is complete but not entirely correct 740 000 565 400 174 600 129 200 45 400 Prior Year 100 0 640 000 76 4 280 000 23 6 360 000 17 5 258 800 6 1 101 200 33 Prior Year 100 0 icate completion 76 4 x 23 6 x 17 5 x 6 1 X Return to quest

Given the uniform distribution below f x 0 1 2 3 4 5 6 7 8 9 10 11 12 X a What is the height of the function f x Give your answer as a reduced fraction b What is the probability of the shaded region Give your answer as a reduced frac

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