. Roll two fair dice. Each die has six faces

.a. List the sample space.

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

c. Let B be the event that the sum of the two rolls is at most seven. Find P(B).

d. In words, explain what P(A|B) represents. Find P(A|B).

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

f. Are A and B independent events? Explain your answer in one to three complete sentences, including numericaljustification.