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Roll two fair dice. Each die has six faces.

a. List the sample space.

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

c. Let 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 and mutually exclusive events? Explain your answer in one to three complete sentences, including numerical justification.

f. Are and independent events? Explain your answer in one to three complete sentences, including numerical justification.

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