Unit 3 Review HOMEWORK
The probability that an event will happen is *P(E) = 20/29*. Find the probability that the event will not happen. (Type answer as either an *integer* or a *simplified fraction*.) The probability that the event will not happen is *____*.
Correct Answer: *⁹/₂₉* (*3.1.17*)
Determine the number of outcomes in the event. Decide whether the event is a simple event or not. *You randomly select one card from a standard deck of 52 playing cards. Event A is selecting a king of diamonds.* Part 1:* Event A has *_* outcome(s). *Part 2:* Is the event a simple event? *__(1)__*, because event A has *___(2)___* one outcome.
Correct Answers: *Part 1:* *1* *Part 2:* *(1):* *Yes,* *(2):* *exactly* (*3.1.35*)
Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. *The probability of choosing 5 numbers from 1 to 42 that match the 5 numbers drawn by a certain lottery is 1/850,668 ≈ 0.00000118.* This is an example of *__(1)__* probability, since *__________(2)__________*.
Correct Answer(s): *(1):* *classical* *(2):* *every combination of 5 numbers has an equal chance of being drawn.* (*3.1.54*)
Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. *According to company records, the probability that a washing machine will need repairs during a ten-year period is 0.29.* This is an example of *__(1)__* probability, since *__________(2)__________*.
Correct Answer(s): *(1):* *empirical* *(2):* *the stated probability is calculated based on observations from the company records.* (*3.1.53*)
Determine which numbers could *not* be used to represent the probability of an event. Select all that apply. A.) −1.5, because probability values cannot be less than 0. B.) 33.3%, this is because probability values cannot be greater than 1. C.) 320/1058, because probability values cannot be in fraction form. D.) 64/25, because probability values cannot be greater than 1. E.) 0.0002, because probability values must be rounded to two decimal places. F.) 0, because probability values must be greater than 0.
Correct Answer(s): A.) −1.5, because probability values cannot be less than 0. D.) 64/25, because probability values cannot be greater than 1. (*3.1.2*)
A random number generator is used to select an integer from 1 to 50 (inclusively). What is the probability of selecting the integer 375? (Type answer as either an *integer* or a *decimal*, but *DO NOT ROUND*.) The probability is *__*.
Correct Answer: *0* (*3.1.11*)
You randomly select an integer from 0 to 49 (inclusively) and then randomly select an integer from 0 to 4 (inclusively). What is the probability of selecting a 3 both times? (Type answer as either an *integer* or a *decimal*, but *DO NOT ROUND*.) The probability is *____*.
Correct Answer: *0.004* (*3.1.13*)
Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a queen and then selecting an eight. (Round to *three* decimal places.) The probability of selecting a queen and then selecting an eight is *____*.
Correct Answer: *0.006* (*3.2.19*)
A probability experiment consists of rolling a fair 6-sided die. Find the probability of the event below (type answer as either an *integer* or a *decimal*, and round to *three* decimal places). *rolling a 1* The probability is *____*.
Correct Answer: *0.167* (*3.1.41*)
A coin is tossed and a six-sided die numbered 1 through 6 is rolled. Find the probability of tossing a head and then rolling a number greater than 2. (Round to *three* decimal places.) The probability of tossing a head and then rolling a number greater than 2 is *____*.
Correct Answer: *0.334* (*3.2.20*)
A probability experiment consists of rolling a fair 8-sided die. Find the probability of the event below (type answer as either an *integer* or a *decimal*, and round to *three* decimal places). *rolling a number greater than 5* The probability is *____*.
Correct Answer: *0.375* (*3.1.43*)
Find P(A or B or C) for the given probabilities. *P(A) = 0.38, P(B) = 0.22, P(C) = 0.19* *P(A and B) = 0.11, P(A and C) = 0.03, P(B and C) = 0.07* *P(A and B and C) = 0.01* P(A or B or C) = *___*
Correct Answer: *0.59* (*3.3.27*)
A physics class has 40 students. Of these, 11 students are physics majors and 18 students are female. Of the physics majors, two are female. Find the probability that a randomly selected student is female or a physics major (round to *three* decimal places). The probability that a randomly selected student is female or a physics major is *____*.
Correct Answer: *0.675* (*3.3.13*)
The probability that an event will happen is *P(E) = 0.16*. Find the probability that the event will not happen. (Simplify the answer.) The probability that the event will not happen is *___*.
Correct Answer: *0.84* (*3.1.18*)
By rewriting the formula for the multiplication rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is *P(B|A) = (P(A and B))/(P(A))*. Use the information below to find the probability that a flight departed on time given that it arrives on time. (Round to the *nearest thousandth* (*three* decimal places).) *The probability that an airplane flight departs on time is 0.89*. *The probability that a flight arrives on time is 0.86*. *The probability that a flight departs and arrives on time is 0.81*. The probability that a flight departed on time given that it arrives on time is *____*.
Correct Answer: *0.942* (*3.2.41*)
By rewriting the formula for the Multiplication Rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is *P(B|A) = (P(A and B))/(P(A))*. Use the information below to find the probability that a flight arrives on time given that it departed on time. (Round to the *nearest thousandth* (*three* decimal places).) *The probability that an airplane flight departs on time is 0.89.* *The probability that a flight arrives on time is 0.86.* *The probability that a flight departs and arrives on time is 0.84.* The probability that a flight arrives on time given that it departed on time is *____*.
Correct Answer: *0.944* (*3.2.42*)
A restaurant offers a $12 dinner special that has 6 choices for an appetizer, 10 choices for an entrée, and 4 choices for a dessert. How many different meals are available when you select an appetizer, an entrée, and a dessert? (Type answer as a *whole *number*.) A meal can be chosen in *___* ways.
Correct Answer: *240* (*3.1.37*)
A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of six digits. The first digit cannot be 3 and the last digit must be even. How many different codes are available? (Note that 0 is considered an even number.) (Type answer as a *whole number*.) The number of different codes available is *______*.
Correct Answer: *45,000* (*3.1.39*)
Of the cartons produced by a company, 5% have a puncture, 3% have a smashed corner, and 1.3% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner (type answer as either an *integer* or a *decimal*, but *DO NOT ROUND*). The probability that a randomly selected carton has a puncture or a smashed corner [is] *__%*.
Correct Answer: *6.7%* (*3.3.15*)
What is the difference between an outcome and an event? Choose the correct answer below. A.) An outcome is the result of a single probability experiment. An event is a set of one or more possible outcomes. B.) An event is the result of a single probability experiment. An outcome is the set of all possible events. C.) An outcome is the result of a single probability experiment. An event is the set of all possible outcomes. D.) An event is the result of a single probability experiment. An outcome is a set of one or more possible events.
Correct Answer: A.) An outcome is the result of a single probability experiment. An event is a set of one or more possible outcomes. (*3.1.1*)
What is the difference between independent and dependent events? Choose the correct answer below. A.) Two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event affects the probability of the occurrence of the other event. B.) Two events are independent when the occurrence of one event affects the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event does not affect the probability of the occurrence of the other event. C.) Two events are independent if they can occur at the same time. Two events are dependent if only one of the two events can occur. D.) Two events are independent if only one of the two events can occur. Two events are dependent if they can occur at the same time.
Correct Answer: A.) Two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event affects the probability of the occurrence of the other event. (*3.2.1*)
If two events are mutually exclusive, why is P(A and B) = 0? Choose the correct answer below. A.) P(A and B) = 0 because A and B each have the same probability. B.) P(A and B) = 0 because A and B cannot occur at the same time. C.) P(A and B) = 0 because A and B are independent. D.) P(A and B) = 0 because A and B are complements of each other.
Correct Answer: B.) P(A and B) = 0 because A and B cannot occur at the same time. (*3.3.1*)
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. *If two events are mutually exclusive, they have no outcomes in common.* Choose the correct answer below. A.) False. If two events are mutually exclusive, they have some outcomes in common. B.) True. C.) False. If two events are mutually exclusive, they have every outcome in common.
Correct Answer: B.) True. (*3.3.3*)
The frequency distribution to the right shows the number of voters (in millions) according to age. Consider the event below. Can it be considered unusual? *A voter chosen at random is between 35 and 44 years old* *Ages of voters* = *Frequency* *18 to 20* = *11.2* *21 to 24* = *9.2* *25 to 34* = *20.3* *35 to 44* = *6.8* *45 to 64* = *15.1* *65 and over* = *83.0* Choose the correct answer below. A.) Yes. The probability of the event is close to 1. B.) Yes. The probability of the event is close to 0. C.) No. The probability of the event is not close to 0. D.) No. The probability of the event is not close to 1.
Correct Answer: B.) Yes. The probability of the event is close to 0. (*3.1.79*)
The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. For example, if the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2:3. The probability of winning an instant prize game is 1/10. The odds of winning a different instant prize game are 1:10. If you want the best chance of winning, which game should you play? Explain your reasoning. Choose the correct answer below. A.) You should play the second game because the probability of winning a game with 1:10 odds of winning is 1/9, which is greater than 1/10. B.) You should play the first game because the probability of winning a game with 1:10 odds of winning is 1/11, which is less than 1/10. C.) You should play the second game because the probability of winning a game with 1:10 odds of winning is 1/11, which is less than 1/10. D.) You should play the first game because the probability of winning a game with 1:10 odds of winning is 1/9, which is greater than 1/10.
Correct Answer: B.) You should play the first game because the probability of winning a game with 1:10 odds of winning is 1/11, which is less than 1/10. (*3.1.91*)
Explain how the complement can be used to find the probability of getting at least one item of a particular type. Choose the correct answer below. A.) The complement of "at least one" is "all." So, the probability of getting at least one item is equal to P(all items) − 1. B.) The complement of "at least one" is "all." So, the probability of getting at least one item is equal to 1 − P(all items). C.) The complement of "at least one" is "none." So, the probability of getting at least one item is equal to 1 − P(none of the items). D.) The complement of "at least one" is "none." So, the probability of getting at least one item is equal to P(none of the items) − 1.
Correct Answer: C.) The complement of "at least one" is "none." So, the probability of getting at least one item is equal to 1 − P(none of the items). (*3.2.4*)
For the given pair of events, classify the two events as independent or dependent. *Getting caught in traffic* *Spilling coffee in the car* Choose the correct answer below. A.) The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other. B.) The two events are dependent because the occurrence of one affects the probability of the occurrence of the other. C.) The two events are independent because the occurrence of one affects the probability of the occurrence of the other. D.) The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.
Correct Answer: D.) The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other. (*3.2.9*)
Decide whether the events shown in the accompanying Venn diagram are mutually exclusive. Explain your reasoning. (Since I don't have Quizlet+, I can't insert the image of the actual Venn diagram; ergo, I pasted the description.) *Sample Space*: *Presidential Candidates* *Blue circle:* Presidential candidates who won in the state of Texas *Pink circle*: Presidential candidates who lost the election *Purple intersection*: *blue* and *pink* overlap The events *_____(1)_____* mutually exclusive, since there *__________(2)__________* and *_______(3)_______*.
Correct Answers: *(1)*: *are not* *(2)*: *is at least 1 presidential candidate who won in the state of Texas* *(3)*: *lost the election.* (*3.3.7*)
Decide whether the events shown in the accompanying Venn diagram are mutually exclusive. Explain your reasoning. (Since I don't have Quizlet+, I can't insert the image of the actual Venn diagram; ergo, I pasted the description.) *Sample Space*: *Movies* *Blue circle:* Movies that are rated R *Pink circle:* Movies that receive mostly negative reviews *Purple intersection:* *Blue* and *Pink* overlap The events *____(1)____* mutually exclusive, since there are *__(2)__* movies that are rated R and *______(3)______*.
Correct Answers: *(1):* *are not* *(2):* *some* *(3):* *receive mostly negative reviews.* (*3.3.8*)
Determine whether the events are independent or dependent. Explain your reasoning. *Returning a rented movie after the due date and receiving a late fee* The events are *___(1)___* because the outcome of returning a rented movie after the due date *__(2)__* the probability of the outcome of receiving a late fee.
Correct Answers: *(1):* *dependent* *(2):* *affects* (*3.2.11*)
In gambling, the chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, if the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2:3 (read "2 to 3") or 2/3. (Note: If the odds of winning are 2/3, the probability of success is 2/5.) The odds of an event occurring are 1:2. Find (a) the probability that the event will occur and (b) the probability that the event will not occur. (Type answers as either an *integer* or a *decimal*, and round to the *nearest thousandth* (*three* decimal places).) *Part 1 (a):* The probability that the event will occur is *____*. *Part 2 (b):* The probability that the event will not occur is *____*.
Correct Answers: *Part 1 (a):* *0.333* *Part 2 (b):* *0.667* (*3.1.93*)
The accompanying table shows the results of a survey in which 250 male and 250 female workers ages 25 to 64 were asked if they contribute to a retirement savings plan at work. Complete parts 1 (a) and 2 (b) below (round answers to *three* decimal places). *Contribute:* *Male (M):* 110 *Female (F):* 150 *Total:* *260* *Do Not Contribute:* *Male (M):* 140 *Female (F):* 100 *Total:* *240* *Total:* *M:* *250* *F:* *250* *"Total":* *"500"* *Part 1 (a):* Find the probability that a randomly selected worker contributes to a retirement savings plan at work, given that the worker is male. The probability that a randomly selected worker contributes to a retirement savings plan at work, given that the worker is male, is *____*. *Part 2 (b):* Find the probability that a randomly selected worker is female, given that the worker contributes to a retirement savings plan at work. The probability that a randomly selected worker is female, given that the worker contributes to a retirement savings plan at work, is *____*.
Correct Answers: *Part 1 (a):* *0.44* *Part 2 (b):* *0.577* (*3.2.8*)
The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. Complete parts 1 (a) and 2 (b) below. (Round answers to *three* decimal places.) *Business Degrees:* *Male (M):* 198,277 *Female (F):* 176,022 *Total:* *374,299* *Nonbusiness Degrees:* *Male (M):* 607,855 *Female (F):* 938,380 *Total:* *1,546,235* *Total:* *M:* *806,132* *F:* *1,114,402* *"Total":* *"1,920,534"* *Part 1 (a):* Find the probability that a randomly selected student is male, given that the student received a business degree. The probability that a randomly selected student is male, given that the student received a business degree, is *____*. *Part 2 (b):* Find the probability that a randomly selected student received a business degree, given that the student is female. The probability that a randomly selected student received a business degree, given that the student is female, is *____*.
Correct Answers: *Part 1 (a):* *0.53* *Part 2 (b):* *0.158* (*3.2.7*)
A stem-and-leaf plot for the number of touchdowns scored by all Division 1A football teams is shown below. Complete parts A (1) through C (3 & 4). *Key: 1 | 5 = 15* 1 | 3 4 5 7 8 8 2 | 0 1 2 2 3 4 5 7 8 8 9 3 | 0 0 1 1 1 2 2 3 3 4 4 5 5 7 7 7 8 9 4 | 0 0 1 2 2 3 4 5 5 5 5 6 7 8 8 9 5 | 0 2 3 5 5 7 8 6 | 1 3 6 7 7 | 8 | 7 *Part 1 (a):* If a team is selected at random, find the probability the team scored at least 33 touchdowns. (Round to *three* decimal places.) *____* *Part 2 (b):* If a team is selected at random, find the probability the team scored between 40 and 48 touchdowns inclusive. (Round to *three* decimal places.) *____* *Part 3 (c):* If a team is selected at random, find the probability the team scored more than 79 touchdowns. (Round to *three* decimal places.) *____* *Part 4 (c):* Are any of these events unusual? Select all the unusual events below. A.) Scoring at least 33 touchdowns is unusual. B.) Scoring more than 79 touchdowns is unusual. C.) Scoring between 40 and 48 touchdowns inclusive is unusual. D.) None of the events are unusual.
Correct Answers: *Part 1 (a):* *0.619* *Part 2 (b):* *0.238* *Part 3 (c):* *0.016* *Part 4 (c):* B.) Scoring more than 79 touchdowns is unusual. (*3.1.87*)
Part 1 (a): List an example of two events that are independent. Part 2 (b): List an example of two events that are dependent. *Part 1 (a):* List an example of two events that are independent. Choose the correct answer below. A.) A father having hazel eyes and a daughter having hazel eyes B.) Rolling a die twice C.) Not putting money in a parking meter and getting a parking ticket D.) Selecting a queen from a standard deck, not replacing it, and then selecting a queen from the deck *Part 2 (b):* List an example of two events that are dependent. Choose the correct answer below. A.) Tossing a coin and getting a head, and then rolling a six-sided die and obtaining a 6 B.) Drawing one card from a standard deck, not replacing it, and then selecting another card C.) Selecting a ball numbered 1 through 12 from a bin, replacing it, and then selecting a second numbered ball from the bin D.) Rolling a die twice
Correct Answers: *Part 1 (a):* B.) Rolling a die twice *Part 2 (b):* B.) Drawing one card from a standard deck, not replacing it, and then selecting another card (*3.2.2*)
Determine the number of outcomes in the event. Decide whether the event is a simple event or not. *A computer is used to select randomly a number between 1 and 9, inclusive. Event A is selecting the number 4.* *Part 1:* Event A has *_* outcome(s). *Part 2:* Is the event a simple event? *__(1)__*, because event A has *__(2)__* one outcome.
Correct Answers: *Part 1:* *1* *Part 2:* *(1):* *Yes,* *(2):* *exactly* (*3.1.33*)
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. *Playing the game of roulette, where the wheel consists of slots numbered 00, 0, 1, 2, ..., 45* *To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots.* *Part 1:* Identify the sample space. A.) The sample space is {1, 2, ..., 45}. B.) The sample space is {00}. C.) The sample space is {00, 0}. D.) The sample space is {00, 0, 1, 2, ..., 45}. *Part 2:* How many outcomes are in the sample space? *__*
Correct Answers: *Part 1:* D.) The sample space is {00, 0, 1, 2, ..., 45}. *Part 2:* *47* (*3.1.27*)
Identify the sample space of the probability experiment (use a *comma* to separate answers, and type them in *ascending (↑)* order) and determine the number of outcomes in the sample space. *Randomly choosing a number from the odd numbers between 20 and 30* *Part 1:* The sample space is {*__*, *__*, *__*, *__*, *__*}. *Part 2:* There are *__* outcome(s) in the sample space.
Correct Answers: *Part 1:* {*21*, *23*, *25*, *27*, *29*} *Part 2:* *5* (*3.1.25*)