You roll a pair of fair six-sided dice. The sample space of 36 possible outcomes is shown below.
Based on this information, answer the following
questions.
What is P(A), the probability that the first
die is a 3?
What is P(B), the probability that the sum
of the dice is 8?
What is P(A and B), the probability that
the first die is a 3 and the sum of the dice is
8?
What is P(
BA), the conditional
probability that the sum of the dice is 8
given that the first die is a 3?
Is P(
BA) = P(B)? Are the events A and
B independent?