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Chapter 5: Q 5.86. (page 216)

Suppose that A and B are events such that P(A)=14,P(B)=13and P(AorB)=12

Part (a). Are event A and B mutually exclusive ? Explain your answer.

Part (b) FindP(A&B)

Short Answer

Expert verified

Part (a) Aand Bare not mutually exclusive because Aand Bare not zero.

Part (b)P(A&B)=112

Step by step solution

01

Part (a) Step 1. Given information.  

P(A)=14P(B)=13P(A&B)=12

02

Part (a) Step 2. The following concept was used:

P(A鈭�B)=P(A)+P(B)-P(A鈭�B)12=14+13-P(A鈭�B)P(A鈭�B)=712-12P(A鈭�B)=112

Aand Bare not mutually exclusive because A and B are not zero.

03

Part (b) Step 1. Given information.  

P(A)=14P(B)=13P(A&B)=12

04

Part (b) Step 2. The following concept was used:

P(A鈭�B)=P(A)+P(B)-P(A鈭�B)12=14+13-P(A鈭�B)P(A鈭�B)=712-12P(A鈭�B)=112

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