Probability
posted by Anna .
One of two cards is black on one side and white on the other side. The second card is black on both sides. One card is selected at random and the side facing up is black. What is the probability that the other side of the card is white?

There are eight possible card arrangements with equal probability. The first of each pair listed below is the first draw. B' is one of the black sides of the twosided black card.
The possibilities are:
B/W and B/B'; B/W and B'/B; W/B and B/B'; W/B and B/B', B/B' and W/B; B/B' and B/W; B'/B and W/B; B'/B and B/W. Six of these possibilities give Black in the first draw. The only possibilities after getting a B or B' are the following six:
B/W and B/B'; B/W and B'/B; B/B' and W/B; B/B' and B/W; B'/B and W/B; B'/B and B/W.
Two of those six result in white for the second draw. The probability of white is 1/3.