The Basic Practice of Statistics
The Basic Practice of Statistics
7th Edition
ISBN: 9781464142536
Author: David S. Moore, William I. Notz, Michael A. Fligner
Publisher: W. H. Freeman
Question
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Chapter 13, Problem 13.45E
To determine

The probability that Connecticut job is offered to Julie but not the New Jersey or federal job.

Expert Solution & Answer
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Answer to Problem 13.45E

The probability that Connecticut job is offered to Julie but not the New Jersey or federal job is 0.35.

Explanation of Solution

Given info:

Julie is offered a job by three events A, B and C. A be the event for Connecticut office of the Chief Medical Examiner, B be the event for the New Jersey Division of Criminal Justice and C be the event for Federal Disaster Mortuary Operations Response Team.

Julie writes some probabilities P(A) is 0.5, P(B) is 0.4, P(C) is 0.2, P(AandB) is 0.1, P(AandC) is 0.05, P(BandC) is 0.05 and P(AandBandC) is 0.

Calculation:

To draw the Venn diagram, find the probabilities.

Calculate the probability for event (Aand(notB)and(notC)) .

P(Aand(notB)and(notC))=P(A)P(AandB)P(AandC)

Substitute 0.5 for P(A) , 0.1 for P(AandB) and 0.05 for P(AandC) in above formula.

P(Aand(notB)and(notC))=0.50.10.05=0.35

Calculate the probability for event (Band(notA)and(notC)) .

P(Band(notA)and(notC))=P(B)P(AandB)P(BandC)

Substitute 0.4 for P(B) , 0.1 for P(AandB) and 0.05 for P(BandC) in above formula.

P(Band(notA)and(notC))=0.40.10.05=0.25

Calculate the probability for event (Cand(notA)and(notB)) .

P(Cand(notA)and(notB))=P(C)P(AandC)P(BandC)

Substitute 0.2 for P(C) , 0.05 for P(AandC) and 0.05 for P(BandC) in above formula.

P(Cand(notA)and(notB))=0.20.050.05=0.1

Calculate the probability for event (neitherAnorBnorC) .

P(neitherAnorBnorC)=1[P(Aand(notB)and(notC))+P(Band(notA)and(notC))+P(Cand(notA)and(notB))+P(AandB)+P(AandC)+P(BandC)+P(AandBandC)]

Substitute 0.35 for P(Aand(notB)and(notC)) ,

0.25 for P(Band(notA)and(notC)) ,

0.1 for P(Cand(notA)and(notB)) , 0.1 for P(AandB) , 0.05 for P(AandC) , 0.05 for P(BandC) and 0 for P(AandBandC) in above formula.

P(neitherAnorBnorC)=1[0.35+0.25+0.1+0.1+0.05+0.05+0]=1[0.9]=0.1

Instructions:

  • Draw a Venn diagram form all the above information.

The Basic Practice of Statistics, Chapter 13, Problem 13.45E

From the Venn diagram it can be noticed that the probability Connecticut job is offered to Julie but not the New Jersey or federal job is 0.35.

Thus, the probability that Connecticut job is offered to Julie but not the New Jersey or federal job is 0.35.

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