Question

Suppose we have 3 cards identical in form except that both sides of the first card are colord red, both sides of the second card are colored black and one side of the third card is colored red and the other side is black. The three cards are mixed up in a hat, and 1 card is randomly selected and put on the ground. If the upper side of the chosen card is colored red, what is the probability that the other side is colored black?

Answer 1

P(upper side of the chosen card is colored red) = P(upper side is red and first card is choosen) + P(upper side is red and second card is choosen) + P(upper side is red and third card is choosen)

                                                      = 1/3 * 1 + 1/3 * 0 + 1/3 * 1/2

                                                      = 0.5

P(other side is colored black | upper side is colored red) = P(other side is colored black and upper side is colored red) / P(upper side of the chosen card is colored red)

                                                                                          = (1/3 * 1/2) / 0.5

                                                                                          = 1/3 (ans)