Suppose events A, B, C have the following probabilities: PCAIB) = , P(Cll) = , P

Question

Suppose events A, B, C have the following probabilities: PCAIB) = , P(Cll) = , P(A n ClB) = . Given that B has occurred, a) (2 marks) Find the probability that only C has occurred. b) (3 marks) Find the probability that only A or only C has occurred, but not both c) (2 marks) Find the probability that A or C has occurred. d) (2 marks) Represent all the probabilities found in (a)-(c) in an appropriately labeled Venn diagram. You 23 3 45 45 may use more than one Venn diagram if you would like to represent each of (a)-(o) separately.

Explanation / Answer

GIven that B has occured.

a) P(only C/B) = P(C/B)-P( A intersecion C/B)= ( 23-11)/45=12/45

b)P( only A/B) = 1/3-11/45=4/45

c)P( A or C) = 12/45+4/45+11/45=0.6

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