Answer each question to the best of your ability. Show your calculations (they can be verified on a calculator). Your final answer should be in the form of a complete sentence.

1. Suppose you randomly select a family with three children. Assume that births of boys and girls are equally likely.

a. How many birth orders are possible? List them in a probability distribution table. (3 points)

b. What is the probability of two boys and a girl? (2 points)

c. What is the probability of a girl, a boy, and a boy (in that order)? (2 points)

d. What is the probability of at least one girl? (2 points)

e. What is the probability of at least two boys? (2 points)

2. Suppose you randomly select a family with four children. Assume that births of boys and girls are equally likely.

a. How many birth orders are possible? List them in a probability distribution table. (3 points)

b. What is the probability that the family has four children of the same gender? (2 points)

c. What is the probability that the family has a boy, a girl, a boy, and a girl (in that order)?

(2 points)

d. What is the probability that the family has two girls and two boys (in any order)? (2 points)