Rework problem 35 from the Chapter 2 review exercises in your text, involving auditioning for a play. For this problem, assume 9 males audition, one of them being Miles, 5 females audition, one of them being Jackie, and 6 children audition. The casting director has 3 male roles available, 1 female role available, and 2 child roles available.

(1) How many different ways can these roles be filled from these auditioners?

(2) How many different ways can these roles be filled if exactly one of Miles and Jackie gets a part?

(3) What is the probability (if the roles are filled at random) of both Miles and Jackie getting a part?

Rework problem 26 from the chapter 3 review section of your text, involving the rolling of two fair dice. Answer the following questions.

(1) What is the probability that the sum is 9, given that at least one of the numbers rolled is even?

(2) What is the probability that at least one number is even, given that the sum is 9?

(3) What is the probability that at least one number is even, given that the sum is 8?

Rework problem 7 of the review problems for Chapter 4 in your textbook, in which three balls are selected simultaneously and randomly from a box. But assume that the box contains 8 red balls and 5 green balls. Also assume that each red ball selected pays $0.30, that each green ball selected pays $0.70, and that it costs $1.10 to play the game. A random variable X

is defined to be the net payoff for a player. How many different values are possible for the random variable X? 4

Fill in the table below to complete the probability density function. Be certain to list the values of X

in ascending order.

Value of X Probability

Assume that a fair six-sided die is rolled 10 times, and the roll is called a success if the result is in {1,2}

.What is the probability that there are exactly 1 successes or exactly 1 failures in the 10 rolls?