Probability of A and B (1 of 2)

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If A and B are Independent
A and B are two events. If A and B are independent, then the probability that events A and B both occur is:

p(A and B) = p(A) x p(B).

In other words, the probability of A and B both occurring is the product of the probability of A and the probability of B.

What is the probability that a fair coin will come up with heads twice in a row? Two events must occur: a head on the first toss and a head on the second toss. Since the probability of each event is 1/2, the probability of both events is: 1/2 x 1/2 = 1/4.

Now consider a similar problem: Someone draws a card at random out of a deck, replaces it, and then draws another card at random. What is the probability that the first card is the ace of clubs and the second card is a club (any club). Since there is only one ace of clubs in the deck, the probability of the first event is 1/52. Since 13/52 = 1/4 of the deck is composed of clubs, the probability of the second event is 1/4. Therefore, the probability of both events is: 1/52 x 1/4 = 1/208 .