Probability of A and B (2 of 2)

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If A and B are Not Independent
If A and B are not independent, then the probability of A and B is:

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

where p(B|A) is the conditional probability of B given A.

If someone draws a card at random from a deck and then, without replacing the first card, draws a second card, what is the probability that both cards will be aces? Event A is that the first card is an ace. Since 4 of the 52 cards are aces, p(A) = 4/52 = 1/13. Given that the first card is an ace, what is the probability that the second card will be an ace as well? Of the 51 remaining cards, 3 are aces. Therefore, p(B|A) = 3/51 = 1/17 and the probability of A and B is:

1/13 x 1/17 = 1/221.

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