An envolope contains three cards A black card that is black

An envolope contains three cards: A black card that is black on both sides, a white card that is white on both sides and a mixed card that is black on one side and white on the other. You select one card on random and note that the card facing up is black. What is the probability that the other side is black?

Solution

P(first side is black) = (1/3)*(1) + (1/3)*(1/2) + (1/3)*(0)

P(first side is black) = 1/2 = 0.5

P(other side is black|first side is black) = P(both sides black)/P(first side is black)

= (1/3)*1/(0.5)

= 2/3 = 0.67