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Chapter 3: Q.3-53E (page 193)

For two events, A and B, P(A)= .4, P(B)= .2 , and P(A鈭�B) = .1:

a. Find P (A/B).

b. Find P(B/A).

c. Are A and B independent events?

Short Answer

Expert verified

Answer

  1. 0.50
  2. 0.25
  3. No

Step by step solution

01

Step-by-Step SolutionStep 1: Introduction

The likelihood of an event occurring if another event has already occurred is conditional probability. The conditional probability formula:

P (A/B) =P (A鈭�B)P (B)

02

Find the probability

P (A/B) =P (A鈭�B)P (B)=.1.2=.50

Hence, the required probability is 0.50.

03

Find the probability

P (B/A) =P (B鈭�A)P (A)=.1.4=.25

Hence, the required probability is 0.25.

04

Identify that A and B are independent events

For independent event P (A鈭�B) = P(A)脳P(B)

HereP(A)脳P(B) = .4脳.2= 0.08, which means P (A鈭�B) = 0.1鈮�0.08.

No, A and B are not independent events.

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