Given that P(A AND B) = 0.29 and P(A | B) = 0.67, what is P(B)?Give your answer as a percent. Round to two decimal places.

Question

asked Jun 28, 2023 341 views

1 Answer

Martin Gunia · Answer 1 · 2023-07-05T14:22:32+0000

According to the given problem,

$\begin{gathered} P(A\cap B)=0.29 \\ P((A)/(B))=0.67 \end{gathered}$

Consider the formula for conditional probability,

$P((A)/(B))=(P(A\cap B))/(P(B))$

Transposing the terms,

$P(B)=(P(A\cap B))/(P((A)/(B)))$

Substitute the values,

$\begin{gathered} P(B)=(0.29)/(0.67) \\ P(B)=(29)/(67) \\ P(B)\approx0.4328 \\ P(B)\approx43.28\text{ percent} \end{gathered}$

Thus, the required probability is 43.28% approximately.