1. Consider rolling a fair 6 faced die twice. Let A be then that the sum of the two rolls is at most 6, and B be the event that the first one is an even number.

- What is the probability that the sum of the two rolls is at most 6 given that the first on is an even number? Show all work and explain your answer.

- Are even A and event B independent? Explain.

2. Let random variable x represent the number of girls in a family of three children.

- construct a table describing the probability distribution

- Determine the mean and standard deviation of x. (round to two decimal places and show all work)

3. Mimi just started her tennis class. On average, she returned 20% of her opponent's serves. assume her opponent serves 10 times. Show all work

- Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n) probability of successes (p) and probability of failures (q), respectively?

- Find the probability that she returns at least 1 of 10 serves from her opponent.