Question 513420: Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.65 and P(B) = 0.35.
What is P(A B)? that symbol between a and b is upsidedown U...
What is P(A | B)?
Answer by drcole(72)   (Show Source):
You can put this solution on YOUR website! That upside down U means intersection. I'll write "A intersection B" or "A and B" here to represent the same thing.
The probability of A and B, P(A and B), is the probability that both events are true at the same time. Notice, however, that we are told that A and B are mutually exclusive events. This means that if one event is true, the other is false, and vice versa. For example, tossing heads and tossing tails with a coin are mutually exclusive events: they cannot both be true at the same time. Now, one way to write with a formula that A and B are mutually exclusive is to write that the probability of their intersection, P(A and B), is 0: the probability that both events are true at the same time is 0. Thus this question is just asking if you understand the relationship between two events being mutually exclusive and the probability of their intersection being 0.
P(A | B) is the conditionally probability of A, given B. In other words, if you already know that B is true, what is the probability of A? In this case, the answer is obvious: A and B are mutually exclusive, so if we already know that B is true, A must be false, so P(A | B) = 0. In general, the formula for P(A | B) is:
P(A | B) = P(A and B)/P(B)
so since P(A and B) = 0, we can deduce P(A | B) = 0 just by plugging into the formula above.
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