Question

Three events A, B and C are defined over a sample space, S. Events A and B are independent. Events A and C are mutually exclusive. Given that P(A)= 0.04, P(B)=0.25, P(C)=0.20 and P(B/C)=0.15. Find for P(C/B)

Answer 1

[(b/c)=0.15)]

Explanation:

Answer 2

Answer: 0.12

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Work Shown:

P(B/C) = P(B and C)/P(C) ... conditional probability formula

P(B and C) = P(C)*P(B/C)

P(B and C) = 0.20*0.15

P(B and C) = 0.03

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P(C/B) = P(C and B)/P(B) .... note the swap of B and C

P(C/B) = P(B and C)/P(B)

P(C/B) = (0.03)/(0.25)

P(C/B) = 0.12

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Extra notes:

• The fact that events A and B are independent is not relevant.
• The fact A and C are mutually exclusive isn't used here either.
• This problem can be solved through Bayes' Theorem.
• Another alternative you can do is to set up a 3 by 3 contingency table to help solve this problem.