Suppose a coin is flipped and a die is rolled

Suppose a coin is flipped and a die is rolled. Let E1 denote the event "the coin shows a tail", let E2 denote the event "the dies shows a 3", and let E3 denote the event "the coin shows heads and the die shows an odd number". Are E1 and E2 mutually exclusive?

A family of four children. Assume that it is equally probable for a boy or a girl to be born. What is the probability of exactly two girls?

Find a recurrence relation and initial conditions that generate a sequence that begins with the given term.

3,6,9,15,24,39,...