Probability distribution

Question

Suppose you buy four boxes of cereal remember that each box has an equal probability of containing any one of seven collector cards what is the probability of getting four identical cards or three identical cards or two identical cards or two pairs of identical cards or four different cards.

Answer 1

Let's work through a simpler, but similar problem which will illustrate the concepts involved. Suppose we have two bags and each bag contains one red marble, one blue marble, and one green marble. What is the probability that we draw one marble from each bag and get the same color? The sample space, S, is the set containing all possible pairings of marbles after we draw one from each bag. Since there are three ways to draw the first marble and three ways to draw the second marble, we see that S contains 3 * 3 = 9 outcomes. The probability of drawing the red marble from the first bag and the red marble from the second bag is 1 / 9 because there is only one way that can happen. Because the same is true of the other colors, the probability of drawing two marbles of the same color is 3(1 / 9) = 1 / 3.