Question

Events A1,A2, and A3 form a partition of sample space S with Pr(A1)=3/7, Pr(A2)=3/7, Pr(A3)=1/7. E...

Events A1,A2, and A3 form a partition of sample space S with Pr(A1)=3/7, Pr(A2)=3/7, Pr(A3)=1/7. E is an event in S with Pr(E|A1)=3/5, Pr(E|A2)=2/5, and Pr(E|A3)=3/5.
What is Pr(E)?
What is Pr(A2|E)?
What is Pr(E')?
What is Pr(A2'|E')?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

We are given

P(A1)=3/7

P(A2)=3/7

P(A3)=1/7

P(E|A1)=3/5

P(E|A2)=2/5

P(E|A3)=3/5

(1)

P(E)=P(A1) P(E|A1)+P(A2) P(E|A2) +P(A3) P(E|A3)

     

P(E)=0.5143

(2)

(3)

(4)

FOR THE ABOVE FORMULA WE CALCULATE

P(A2')=1-P(A2) = 1-3/7=4/7

P(E')=0.4857

P(E'|A2')=0.4

PUTTING THESE VALUES IN FORMULA

SO

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