Question 1

A fair coin is flipped three times. What is the probability of getting exactly two heads?

Accepted Answer

$$\frac{3}{8}$$

Question 2

If $$P(A) = 0.326$$, what is the probability of the complement of $$A$$, $$P(A')$$?

Accepted Answer

$$0.674$$

Question 3

A standard deck of 52 cards is shuffled. What is the probability that a randomly drawn card is a face card or a spade?

Accepted Answer

$$\frac{19}{26}$$

Question 4

In a town, 28% of voters are Democrats. If two voters are randomly selected for a survey, what is the probability that both are Democrats?

Accepted Answer

$$0.078$$

Question 5

You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. What is the probability that the first card is a King and the second card is a Queen?

Accepted Answer

$$\frac{4}{663}$$

Question 6

An unprepared student makes random guesses for the ten true-false questions on a quiz. What is the probability that there is at least one correct answer?

Accepted Answer

$$0.999$$

Question 7

Two airlines have the following on-time vs late flights: Podunk Airlines: on-time 33, late 6. Upstate Airlines: on-time 43, late 5. If one of the 87 flights is randomly selected, what is the probability that the flight selected arrived on time?

Accepted Answer

$$\frac{76}{87}$$

Question 8

How many different 5-person subcommittees can be formed from a board of 10 directors?

Accepted Answer

$$252$$

Question 9

A musician plans to perform 5 selections. In how many ways can she arrange the musical selections?

Accepted Answer

$$120$$

Question 10

Identify the given random variable as discrete or continuous: The number of oil spills occurring off the Alaskan coast in a year.

Accepted Answer

Discrete

Question 11

A focus group of 10 people is randomly selected. The mean number who recognize a brand is 4.8 with standard deviation 0.89. Would it be unusual to find greater than 9 who recognize the brand?

Accepted Answer

Yes

Question 12

Given a probability table for $$x = $$ number of girls in 14 births (table omitted), find $$P(x \geq 9). $$Assume $$P(x \geq 9) = 0.122.$$

Accepted Answer

$$0.122$$

Question 13

Use the binomial probability formula: $$n = 10$$, $$x = 2$$, $$p = 1/3. $$Find $$P(x = 2).$$

Accepted Answer

$$0.195$$

Question 14

Find the probability of at least 2 girls in 7 births. Assume $$p = 0.5.$$

Accepted Answer

$$0.938$$

Question 15

A brand has recognition rate 48% in a town. From a random sample of 10, find the probability that the number who recognize it is not 4.

Accepted Answer

$$0.780$$

Question 16

Find the standard deviation $$\sigma$$ for a binomial distribution with $$n = 43$$ and $$p = 3/5.$$

Accepted Answer

$$3.21$$

Question 17

According to a college survey, 22% of all students work full time. Find the mean for the number who work full time in samples of size 16.

Accepted Answer

$$3.52$$

Question 18

Using the context of the previous question, find the standard deviation for the number who work full time in samples of size 16.

Accepted Answer

$$1.7$$

Question 19

A medical test for a rare disease has a 98% true positive rate and a 2% false positive rate. If 1% of the population has the disease, what is the probability that a randomly selected person who tests positive actually has the disease? (Use Bayes' theorem.)

Accepted Answer

$$0.33$$

Question 20

A die is rolled twice. What is the probability that the sum is 7?

Accepted Answer

$$\frac{1}{6}$$

Probability and Distributions: Key Concepts and Applications

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