1. Determine if the following is a discrete probability distribution. Justify your answer.

a. x P(x)

0 0.04

1 0.33

3 0.42

4 0.19

5 0.02

b. x P(x)

-1 0.48

3 0.22

5 0.14

6 0.15

2. Fill out the blank to make the given table a discrete probability distribution.

x P(x)

0 0.03

1 0.14

2 0.65

3

4 0.08

3. For the discrete probability distribution below find the mean, variance, and standard deviation.

x P(x)

0 0.15

1 0.20

2 0.35

3 0.22

4 0.07

5 0.01

blank blank

4. The probability distribution shows the cups of beer American Adults consume every week.

Find the expected value of cups of wine American Adults consumes every week.

x P(x)

0 0.4

1 0.1

2 0.3

5 0.12

10 0.05

5. Given the number of trials and the probability of success, determine the probability indicated:

a. n = 15, p = 0.4, find P(4 successes)

b. n = 12, p = 0.2, find P(2 failures)

c. n = 20, p = 0.05, find P(at least 3 successes)

6. An FBI survey shows that about 30% (i.e., 0.3) of all property crimes go solved. Suppose that in New York City 15 such crimes are committed and they are each deemed independent of each other.

a What is the probability that exactly 3 of these 15 crimes will be solved?

b What is the probability that at most 3 of these 15 crimes will be solved?

c What is the probability that more than 11 of these 15 crimes will be solved?

7. A company makes Citi bikes. 95% (i.e., 0.95) pass final inspection. Suppose that 5 bikes are randomly selected.

a What is the probability that exactly 4 of these 5 sports bikes pass final inspection?

b What is the probability that less than 3 of these 5 sports bikes pass final inspection?

8. The BMCC math club has 50 members.

a. In how many different ways can it select a group of 4 members?

b. In how many different ways can it elect a president, vice-president, secretary and treasurer? One member CANNOT hold more than one job.

9. There are 8 different cell phones in total.

a. You want to buy two cell phones. In how many ways can a group of two cell phones be selected?

b. You want to buy two cell phones. One cell phone is for your mom and the other one is for your dad. How many different ways are there?