Question

For two events, A and B, P(A)=.4 , P(B)= .2, and P(A/B)= .6:

a. Find $\mathbf{\text{P (A}}\mathbf{\cap }\mathbf{\text{B)}}$.

b. Find P(B/A).

Short answer

Answer

1. 0.12
2. 0.3

Step-by-step solution

Step-by-Step SolutionStep 1: Introduction

The possibility of an event or outcome occurring dependent on the existence of a preceding event or outcome is referred to as conditional probability. It is determined by multiplying the chance of the previous event by the renewed likelihood of the next, or conditional, occurrence.

Step 2: Find the probability

Here, we have

P(A)=.4

P(B)= .2

P(A/B)= .6:

The probability of$\mathbf{\text{P (A}}\mathbf{\cap }\mathbf{\text{B)}}$:

$\begin{array}{c}\mathbf{\text{P (A}}\mathbf{\cap }\mathbf{\text{B) = P (A/B) x P(B)}}\\ \mathbf{\text{= .6 x .2}}\\ \mathbf{\text{= .12}}\end{array}$

Hence, the required probability of 0.12

Find the probability

$\begin{array}{c}\mathbf{\text{P (B/A) =}}\frac{\mathbf{\text{P (B}}\mathbf{\cap }\mathbf{\text{A)}}}{\mathbf{\text{P (A)}}}\\ \mathbf{\text{=}}\frac{\mathbf{\text{.12}}}{\mathbf{\text{.4}}}\\ \mathbf{\text{=.3}}\end{array}$

Hence, the required probability of 0.3