# Multiplying dependent probabilities

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### Problem

Suppose that Erika simultaneously rolls a six-sided die and a four-sided die. Let A be the event that she rolls doubles and B be the event that the four-sided die is 4. Use the sample space of possible outcomes below to answer each of the following questions.
What is P, left parenthesis, A, right parenthesis, the probability that Erika rolls doubles?
What is P, left parenthesis, B, right parenthesis, the probability that the four-sided die is 4?
What is , the probability that Erika rolls doubles, given that the four-sided die is 4?
What is , the probability that the four-sided die is 4, given that Erika rolls doubles?
What is P, left parenthesis, A, space, a, n, d, space, B, right parenthesis, the probability that Erika rolls doubles and the four-sided die is 4?
What is ?
What is ?
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