Discrete Probability Distributions

Suppose you roll two fair dice separately. Each die has six faces showing the numbers 1 to 6.

1. List the sample space.

2. Let A be the event that either a three or four is rolled first, followed by an even number. Find the probability of such an event, P(A).

3. Let B be the event that the sum of the two rolls is at most seven. Find the probability of such an event, P(B).

4. Using words, explain what "P(A|B)" represents. Find P(A|B).

5. Are A and B mutually exclusive events? Explain your answer in one to three complete sentences, including numerical justification.

6. Are A and B independent events? Explain in one to three complete sentences, including numerical justification.