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Chapter 3: Q. 120 (page 231)

Given events J and K: P(J) = 0.18; P(K) = 0.37; P(J OR K) = 0.45

a. Find P(J AND K).

b. Find the probability of the complement of event (J AND K).

c. Find the probability of the complement of event (J OR K).

Short Answer

Expert verified

a.P(JANDK)=0.10

b.P((JANDK)')=0.90

c.P((JORK)')=0.55

Step by step solution

01

Given information

Given events J and K: P(J) = 0.18; P(K) = 0.37; P(J OR K) = 0.45

02

Explanation (part a)

we know that

P(JORK)=P(J)+P(K)-P(JANDK)

On rearranging,

P(JANDK)=P(J)+P(K)-P(JORK)

Plugging the given values, we get

localid="1650389819200" P(JANDK)=0.18+0.37-0.45P(JANDK)=0.10

03

Explanation (part b)

the probability of the complement of event (J AND K):

P((JANDK)')=1-P(JANDK)P((JANDK)')=1-0.10P((JANDK)')=0.90

04

Explanation (part c)

the probability of the complement of event (J OR K):

P((JORK)')=1-P(JORK)P((JORK)')=1-0.45P((JORK)')=0.55

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Most popular questions from this chapter

Forty-eight percent of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55%prefer life in prison without parole over the death penalty for a person convicted of first degree murder. 37.6%of all Californians are Latino. In this problem, let: 鈥� C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. L = Latino Californians. Suppose that one Californian is randomly selected.

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