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Chapter 3: Q3-52E (page 193)

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

a. Find P (A∩B).

b. Find P(B/A).

Short Answer

Expert verified

Answer

  1. 0.12
  2. 0.3

Step by step solution

01

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.

02

Step 2: Find the probability

Here, we have

P(A)=.4

P(B)= .2

P(A/B)= .6:

The probability ofP (A∩B):

P (A∩B) = P (A/B) x P(B)= .6 x .2= .12

Hence, the required probability of 0.12

03

Find the probability

P (B/A) =P (B∩A)P (A)=.12.4=.3

Hence, the required probability of 0.3

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