# Tricky Conditional Probability Question

#### statistician

Hi,

Having trouble with the following conditional probability question, please see the attachment below titled Capture1.

Any help would be appreciated.

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#### romsek

Math Team
either $A$ happened or it didn't, $A$ and $\bar{A}$ are mutually exclusive events, so

$P=P[B|A] + P[B|\bar{A}] = 0.2 + 0.7 = 0.9$

$P[A|B] = \dfrac{P[B|A]P[A]}{P} = \dfrac{(0.2)(0.8 )}{0.9} \approx 0.178$