One die has 4 red and 2 white sides; a second has 2 red and 4 white sides.

(a) If we pick a die at random and roll it, what is the probability that the result is a red side?

(b) If the first result is a red side and we roll the same die again, what is the probability of a second red side?

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(a) Let A ="a red side turns up," B "the first die is picked." = P(A) = P(A|B)P(B) +P(AB)P(B) 4 1 2 1 + 62 == For part (b) we compute P(A2|A1) - = 62 P(AA) = P(A A |B)P(B) + P(A ^ A |B)P(B) 2 1 2 1 = ( (1) - + ( 1 ) . . - 6 2 6 2 = 1/2 P(AA) 5/18 P(A) 1/2 = = 5/18 = 5/9