Probability of A and B (1 of 2)
If A and B are Independent
A and B are two events. If A and B are
, 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.
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 .