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 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')?

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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