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Chapter 3: Q98SE (page 203)

Two events, A and B, are independent, withP(A)=.3andP(B)=.1.

a.Are A and B mutually exclusive? Why?

b.FindP(A/B)andP(B/A).

c.FindP(A∪B).

Short Answer

Expert verified

a. No, event A and B are not mutually exclusive.

b.The values arePA/B=0.3 and PB/A=0.1.

c. The value ofPA∪B is 0.37.

Step by step solution

01

Definitions

The events are said to be mutually excusive that event that cannot occurs at the same time and having probability is zero.

The events are said independent if their probability does not affect each another.P(A|B)=P(A)ORP(B|A)=P(B). AndP(A∩B)=P(A).P(B)

The require formula for union isP(A∪B)=P(A)+P(B)-P(A∩B).

02

Find A and B mutually exclusive

a.

Since the events are independent P(A|B)≠P(A).

Thus, event A and B are not mutually exclusive.

03

Find P(A/B) and P(B|A).

b.

PA\B=PA⌒BPB=PA.PBPB=0.3PB\A=PA⌒BPB=PA.PBPA=0.3

So, the values arePA\B=0.3 andPB\A=0.1

04

Find 

c.

Here,

PA∩B=PA.PB=0.30.1=0.03

PA∪B=PA+PB-PA∩B=0.3+0.1-0.03=0.37

Therefore, the value of PA∪Bis 0.37.

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Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities:

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