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

Question

asked Jun 5, 2023 139k views

1 Answer

Uneducatedguy · Answer 1 · 2023-06-10T22:45:43+0000

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