Tricky Conditional Probability Question

Aug 2019
1
0
Australia
Hi,

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

Any help would be appreciated.
 

Attachments

romsek

Math Team
Sep 2015
2,885
1,609
USA
either $A$ happened or it didn't, $A$ and $\bar{A}$ are mutually exclusive events, so

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

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