Chapter 5 Quiz

A probability distribution is given below. What is the value of the missing number. Happy = 0.4 Sad = 0 Angry = 0.2 Confused = 0.14 Sleepy = ????

0.26

60% of people like apples. Of those people who like apples, 45% also like pears. Of those people who do not like apples, 25% like pears. What is the probability that a person likes both apples and pears?

0.27

4% of newborns are born with red hair and 10% have blue eyes and 1.2 percent of newborns have both. What is the probability that a baby has red hair, given that she has blue eyes?

12%

Given the probabilities P(B) = 0.2 and P(AUB) = 0.8, what is P(A) if A and B are mutually exclusive (disjoint)? A. 0.6 B. 0.16 C. 2/8 D. 1 E. 6/8

A. 0.6

Given two events, E and F, such that P(E) = 0.340, P(F) = 0.450, and P(E U F) = 0.637 , then the two events are A. Independent and disjoint (mutually exclusive) B. Independent, but not disjoint (mutually exclusive) C. Disjoint (mutually exclusive), but not independent D. Neither independent nor disjoint (mutually exclusive) E. There is not enough information to answer this question

B

It is estimated that 20% of all drivers do not signal when changing lanes. In a random sample of four drivers, what is the probability that at least one doesn't signal when changing lanes? A. 1 - (.2)^4 B. 1 - (.8)^4 C. (.2)(.8)^3 D. (.2)^3(.8) E. .2

B

6% of all Californians are black. 45% of black Californians support the death penalty, whereas 68% of non-black Californians support the death penalty. Of the Californians who support the death penalty, what percentage of them are black? A. 0.0900 B. 0.0270 C. 0.0405 D. 0.0882 E. 0.0397

C

Suppose P(X) = 0.25 and P(Y) = 0.40. If P(X/Y) = 0.20, what is P[Y/X)? A. 0.10 B. 0.125 C. 0.32 D. 0.45 E. 0.50

C. 0.32

Six Republicans and four Democrats have applied to two open positions on a planning committee. Since all the applicants are qualified to serve, the mayor decides to pick the two new members randomly. What is the probability that both come from the same political party? A. 66/90 B. 52/90 C. 52/100 D. 42/90 E. 42/100

D

You wonder if TV ads are more effective when they are longer or repeated more often or both. So you design an experiment. You prepare 30-second and 60-second a subjects all watch the same TV program, but you assign them at random to four groups. One group sees that 30-second ad once during the program; another sees it three times; the third group sees the 60-second ad once; and the last group sees the 60-second add three times. You ask all subjects how likely they are to buy the camera. A. This is a randomized block design, but not a matched pairs design. B. This is a matched pairs design. C. This is a completely randomized design with one explanatory variable (factor). D. This is a completely randomized design with two explanatory variables (factors). E. This is a completely randomized design with four explanatory variables (factors).

D

Name two events that are definitely mutually exclusive, and two other events that are definitely not mutually exclusive. Explain the difference between the two.

Mutually Exclusive: being a lion and being a giraffe (because they can't both happen) Not Mutually Exclusive: being amazing and being a teacher (because your teacher can be both)

A study by the University of Texas examined a sample of 626 people to see if there was an increased risk of contracting hepatitis C associated with having a tattoo. If the subject had a tattoo, researchers asked whether it had been done in a commercial tattoo parlor or elsewhere. The table below summarizes their findings: Tattoo done in commercial parlor and has hepatitis C = 17 Tattoo done in commercial parlor and no hepatitis C = 35 Tattoo done elsewhere and has hepatitis C = 8 Tattoo done elsewhere and no hepatitis C: 53 No tattoo and has hepatitis C = 18 No tattoo and no hepatitis C = 495 Joann was in the survey and she has Hepatitis C. What is the probability she does not have a tattoo?

P(tattoo I Hep C) = 18/43 = 0.419

The Mars candy company starts a marketing campaign that puts a plastic game piece in each bag of M&Ms. 30% of the pieces show the letter 'M', 20% show the symbol '&', and the rest just say try again. When you collect a set of 3 symbols M, &, and M, you can turn them in for a free bag of candy. Horace, has bought 6 bags of M&Ms. We want to know how likely it is to be a winner. a. Explain how you will use the random numbers listed below to conduct your simulation. b. Conduct one trial on the digits below. State the result of your trial. 36126 70899

a. select 6 digits. see if you have two Ms and one "&" 1, 2, 3: M 4, 5: & 6, 7, 8, 9, 0: nothing b. Horace doesn't win (in this trial, at least)

The Centers for Disease Control say that about 30% of high school students smoke tobacco. Suppose you randomly select high school students to survey them. i. What is the probability none of the first 4 students you interview is a smoker? ii. What is the probability that the first smoker is the sixth person you choose? iii. What is the probability that at least one of 5 chosen students is a smoker? iv. If 3 students are selected, what is the probability that not all of them are smokers?

i. .2401 ii. .05 iii. .832 iv. .973

You are up for your annual job performance review. You estimate there's a 30% chance you'll get a promotion, a 40% chance of a raise, and a 20% chance of getting both a raise and a promotion. i. What is the probability that you will get a raise or a promotion? ii. What is the probability you get a raise but not a promotion? A. 40% B. 10% C. 50% D. 30% E. 20% iii. Are the raise and the promotion independent events? Justify your answer by using probability.

i. 0.5 ii. 20% iii. Not independent

Alicia wants to know how much stores in Anne Arundel County are charging for a Wii U. Below are different ways she could gather her data. Name the design for each method. i. Alicia randomly selects a major city in Anne Arundel County and samples all the stores in that city that sell Wii U. ii. Alicia randomly visits one store in each town in the county. iii. Alicia goes to every store that sells Wii U. iv. Alicia asks her friends who have bought a Wii U which store they went to and how much they paid. v. Alicia puts the names of all the stores in the county into a hat and randomly selects 20 stores.

i. cluster ii. stratified iii. census iv. convenience v. SRS