Independent and Mutually Exclusive Events

The probability for event A is 0.3, the probability for event B is 0.5, and the probability of events A and B is 0.25. Are the events independent?

No because P (A) times P (B) is not equal to P (A and B)

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? 0.09

0.62

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?

1/125

A six-sided number cube is rolled twice. What is the probability that the first roll is an even number and the second roll is a number greater than 4?

1/6

When a softball player gets a hit, it can be a single, double, triple, or home run. When Josephine is at bat, the probability that she hits a single is 15 percent and the probability that she hits a double is 5 percent. What is the probability that Josephine hits a single or a double when she is at bat?

20 percent

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?

5 percent

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?

No, because P(F ∩ T) ≠ P(F) • P(T).

A day of the week is randomly chosen. What is the probability of choosing Monday or a day that starts with the letter S?

P(Monday) = 1/7 P(starts with S) = 2/7 P(Monday or starts with S) = 3/7

A spinner contains four equally shaded areas, as shown below. Louise spins the spinner twice. Which probabilities are correct? Check all that apply.

P(both green) = 1/16 P(both blue) = 1/4 P(first orange and then blue) = 1/8

Which scenario depicts two independent events?

The school play opens tonight and it is raining.

Deepak randomly chooses two marbles from the bag, one at a time, and replaces the marble after each choice. What is the probability he will choose one green marble and then one red marble? Express the probabilities in fraction form.

P(green) = 5/14 P(red) = 2/14 P(green and red) = 5/98

An airline gathers data on late departures and early arrivals over a month. It finds that the probability of a late departure is 12 percent, the probability of an early arrival is 27 percent, and the probability of both a late departure and an early arrival is 4 percent. Which equation shows how to correctly calculate the probability of a late departure or an early arrival?

P(late departure or early arrival) = 0.12 + 0.27 - 0.04

Which scenario depicts two independent events?

The girls' basketball team is playing against the boys' basketball team. The coach chooses a captain for the girls' team and then chooses a captain for the boys' team.

Every person has blood type O, A, B, or AB. A random group of people are blood-typed, and the results are shown in the table.

Use the table to determine the following probabilities. The probability that a randomly chosen person from this group has type B is 3/25 The probability that a randomly chosen person from this group has type AB is 1/25 The probability that a randomly chosen person from this group has type B or type AB blood is 4/25

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?

ends with an r and has five or fewer letters

Consider a single spin on the spinner shown below Which events are mutually exclusive? Check all that apply.

landing on a shaded portion and landing on an unshaded portion

Which events are independent? Check all that apply.

*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. *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.

A bag contains eleven equally sized marbles, which are numbered. Two marbles are chosen at random and replaced after each selection. What is the probability that the first marble chosen is shaded and the second marble chosen is labeled with an odd number?

24/121

The Hawaiian language has 12 letters: five vowels and seven consonants. Each of the 12 Hawaiian letters are written on a slip of paper and placed in the bag. A letter is randomly chosen from the bag and then replaced. Then, a second letter is randomly chosen from the bag. What is the probability that two vowels are chosen?

25/144

A month of the year is chosen at random. What is the probability that the month starts with the letter J or the letter M?

5/12