Question

Hello,Can you please help me with this question? I appreciate your help.Thank you.

Answer 1

Given

P(A)=0.35

P(A')=0.65

P(B|A)=0.5

P(B|A')=0.7

Then, the probability of event A, given that event B has occurred is given by:

`P(A|B)=(P(A)\cdot P(B|A))/(P(A)\cdot P(B|A)+P(A^(\prime))\cdot P(B|A^(\prime)))`

Substitute the given probabilities:

`P(A|B)=((0.35)\cdot(0.5))/((0.35)\cdot(0.5)+(0.65)\cdot(0.7))`

Multiplying:

`\begin{gathered} P(A|B)=(0.175)/(0.175+0.455) \\ P(A|B)=(0.175)/(0.63)=0.278 \end{gathered}`

Answer: 0.278