Assume that A and B are events in a sample space and that P(A) = .40 and P(B|A) = .25. How do you find P(A intersection B)?

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Answer 1 · 2017-02-24T19:20:23

$P( A nn B) = 0.1$

We use the definition of conditional probability:

$P(A|B) = (P( A nn B)) / (P(B))$

So swapping the roles of $A$ and $B$ we get:

$P(B|A) = (P( B nn A)) / (P(A))$

We are given that $P(B|A)=0.25$ , and $P(A)=0.40$ , so:

$0.25 = (P( A nn B)) / 0.40 => P( A nn B) = 0.25 * 0.40 = 0.1$