Question

P(A)=0.31P(B)=0.48P(A and B)=0.21Find P(B|A).Round your answer to two decimal places.

Answer 1

Answer: $P\left(B|A\right)\text{ = 0.68}$

Explanation:

Given:

P(A) = 0.31

P(B) = 0.48

P(A and B) = 0.21

To find:

P(B|A)

The conditional probability P(B|A) is given as:

$\begin{gathered} P\left(B|A\right)=\text{ }\frac{P(B\text{ and A\rparen}}{P(A)} \\ \\ P\left(B|A\right)=\text{ }\frac{P(A\text{ and B\rparen}}{P(A)} \end{gathered}$$\begin{gathered} P\left(B|A\right)\text{ = }\frac{0.21}{0.31}\text{ = 0.6774} \\ \\ P\left(B|A\right)\text{ = 0.68} \end{gathered}$