Suppose that P(A) = 0.3 and P(B) = 0.25 and P(A ∩ B) = 0.1. What is P(B | A(complement))?

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Answer 1 · 2017-02-24T20:04:54

$P(B|A') = 0.5$

We use the definition of conditional probability:

$P(X|Y) = (P(X nn Y)) / (P(Y))$

along with

$P(X nn Y') = P(X) - p(X nn Y)$

From this we get;

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

And

$P(B nn A') = P(B) - P(B nn A)$

We are given that $P(A)=0.3$ , $P(B)=0.25$ and $P(A nn B)=0.1$ , so:

$P(A) \ \ \ \ \ \ \ \ \ \=0.3 => P(A')=0.7$
$P( B nn A') = 0.25 - 0.1 = 0.15$

Hence;

$P(B|A') = 0.15 /0.3 = 0.5$