The probability that two randomly selected cards, from a set of two red and two black cards, are the same color is 1/3. If you list the 24 equally probable permutations of the four cards, then pick any two positions (for example second and fourth cards), you will find eight cases in which the two cards match in color. One way to see that this probability of 8/24 or 1/3 is correct is to consider one of the two chosen cards. Assume that it is red. Of the remaining three cards only one is red, and so the probability that the second chosen card will be red is 1/3. Of course, the same argument applies if the first card is black. Most people guess that the odds are even, when actually they are two to one in favor of the cards' having different colors.

0 0

Post a comment