Independent and Mutually Exclusive Events

Question 1

Which events are independent? Check all that apply.Each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. Sarah picks a number less than 5, keeps it, and then picks an odd number.A number cube is rolled and a spinner is spun. Henry rolls a multiple of 2 and lands on a red portion of the spinner.Two cards are randomly chosen from a standard deck. Eliza chooses a jack, replaces it, and then chooses a black card.Two pairs of socks are randomly chosen from a drawer. Hayden chooses a black pair of socks, puts them on, and then chooses another black pair.A card is randomly chosen from a standard deck and a dart is randomly thrown. Olivia chooses an ace and the dart hits the bull’s-eye.

Revolt · Accepted Answer

B: A number cube is rolled and a spinner is spun. Henry rolls a multiple of 2 and lands on a red portion of the spinner.; C: Two cards are randomly chosen from a standard deck. Eliza chooses a jack, replaces it, and then chooses a black card.; E: A card is randomly chosen from a standard deck and a dart is randomly thrown. Olivia chooses an ace and the dart hits the bull’s-eye.

Question 2

A pharmaceutical company collects data on the side effects participants report for a drug it is testing. The company finds that the probability of experiencing a headache is 5 percent and the probability of experiencing both a headache and heartburn is 2 percent. If the probability of experiencing a headache or heartburn is 8 percent, what is the probability of experiencing heartburn?

Revolt · Accepted Answer

A: 1 percent

Question 3

Louise spins the spinner twice. Which probabilities are correct? Check all that apply.

Revolt · Accepted Answer

A: P(both green) =; B: P(both blue) =; D: P(first orange and then blue) =

Question 4

The names of the months are each written on a slip of paper. If a slip of paper is randomly drawn, which scenario depicts mutually exclusive events?

Revolt · Accepted Answer

B: ends with an r and has five or fewer letters

Question 5

This week in school, there is a 75 percent probability of having a fire drill, a 50 percent probability of a tornado drill, and a 25 percent probability of having both drills. Let event F be a fire drill and event T be a tornado drill. Are the two events independent?

Revolt · Accepted Answer

A: No, because P(F ∩ T) ≠ P(F) • P(T).

Question 6

Events A and B are mutually exclusive. Events B and C are non-mutually exclusive. Which Venn diagram could represent this description?

Revolt · Accepted Answer

D: Option D

Question 7

Josiah takes a multiple-choice quiz that has three questions. Each question has five answer options. If he randomly chooses his answers, what is the probability that he will get all three correct?

Revolt · Accepted Answer

C: StartFraction 1 Over 125 EndFraction

Question 8

Use the table to determine the following probabilities. The probability that a randomly chosen person from this group has type B is . The probability that a randomly chosen person from this group has type AB is . The probability that a randomly chosen person from this group has type B or type AB blood is .

Revolt · Accepted Answer

B: 3/25

Question 9

The probability of event A is 0.48, the probability of event A and B is 0.21, and the probability of events A or B is 0.89. What is the probability of event B?

Revolt · Accepted Answer

D: 0.62

Question 10

Question 10

Revolt · Accepted Answer

A: 1/25

Independent and Mutually Exclusive Events Answers

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