1. In how many ways can 5 starting positions on a basketball team be filled with 10 men whom can play any positions?

2. Nine people are going on a skiing trip in 3 cars that can hold 2, 4, 5passengers respectively. In how many ways is it possible to transport 9 people to the ski lodge, using all cars?

3. The Detroit Music Company has purchased the rights to 10 different songs and it plans to release a new CD with 5 of them.

a) How many different CDs are possible if the order of the songs is important?

b) How many different CDs are possible if the order of the songs is not important?

4. From a group of 4 men and 5 women, how many committees of size 3 are possible

a) With no restrictions?

b) With 1 man and 2 women?

c) With 2 men and 1 woman if a certain man must be on the committee?

5. Wood County sheriff classifies crimes by age (in years) of criminal and whether the crime is violent or nonviolent. As shown below, a total of 150 crimes were reported by the sheriff last year.

a) What is the probability of selecting a case to analyze and finding it involved a violent crime?

b) What is the probability of selecting a case to analyze and finding the crime was committed by someone less than 40 years old?

c) What is the probability of selecting a case that involved a violent crime or an offender less than 20 years old?

d) Given that the violent crime is selected for analysis, what is the probability the crime was committed by a person under 20 years old?

e) Two crimes are selected by a Judge. What is the probability both are violent crimes?

6. A consulting firm rents cars from three agencies, 20% from agency D,20% from agency E, and 60% from agency F. If 10% of the cars from D, 12%of the cars from E, and 4%of the cars from F had bad tires, what is the probability that:

a. the firm will get a car with bad tires?

b. a car with bad tires came from agency F?

7. Consider the following joint probability density function of the random variables X and Y.

f (x, y) = (3x – y)/9 for 1 < x < 3 and 1 < y < 2

a. Find the marginal distributions of X and Y.

b. Are X and Y independent?

c. Find P (X > 2)

8. A dealer’s profit in units of $5,000 on a new automobile is a random variable X having density function.

f (x, y) = 2(1 – x) for -1 ≤ x ≤ 1

a. Find the variance in the dealer’s profit.

b. Demonstrate that Chebyshev’s inequality holds for k = 2 with density function above.

c. What is the probability that the profit exceeds $500?

9. In testing a certain kind of truck tire over a rugged terrain, it is found that 25 % of the trucks fail to complete the test run without a blowout. Of the next 15 trucks tested, find the probability that

a. none will fail the test?

b. at least 2 will fail the test?

c. more than 2 will fail the test?

10. A paediatric nurse is studying the number of babies born at a hospital with congenial defects. Data shows that on the average, one baby with a congenial defect is born per month.

a) What type of probability distribution is appropriate for this problem?

b) Find the expected number of babies born in one year with congenial defects.

c) Find the standard deviation of the number of babies born in one year with congenial defects.

d) Find the probability that no babies are born with congenial defects in one year.

e) Find the probability that at least one baby is born with congenial defects in a year.

f) Find the probability that exactly 12 babies are born with congenial defects in a year.