EBK THE BASIC PRACTICE OF STATISTICS
EBK THE BASIC PRACTICE OF STATISTICS
7th Edition
ISBN: 8220103935319
Author: Moore
Publisher: YUZU
Question
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Chapter 13, Problem 13.44E
To determine

The probability that any of the three jobs is not offered to Julie.

Expert Solution & Answer
Check Mark

Answer to Problem 13.44E

The probability that any of the three jobs is not offered to Julie is 0.1.

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.

EBK THE BASIC PRACTICE OF STATISTICS, Chapter 13, Problem 13.44E

From the Venn diagram it can be noticed that the probability probability that any of the three jobs is not offered to Julie is 0.1.

Thus, the probability that any of the three jobs is not offered to Julie is 0.1.

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