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in Statistics and probability by (54.8k points)

For three events A, B and C

P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs)

P(Exactly one of C or A occurs) = 1/4 and

P(All the three events occur simultaneously) = 1/16.

Then the probability that at least one of the events occurs, is: 

(A) 7/16 

(B) 7/64 

(C) 3/16 

(D) 7/32

1 Answer

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Best answer

Answer is (A) 7/16

We have P(Exactly one of A or B occurs) = P(A)  + P(B) − 2P (A ∩ B) = 1/4

P(Exactly one of B or C occurs) = P(B) + P(C) - 2P(B ∩ C)  = 1/4

P(Exactly one of C or A occurs) = P(C) + P(A) - 2P(C ∩ A) = 1/4

Adding all, we get

Now, it is given that all the three events occur simultaneously, which is given by

P(A ∩ B ∩ C = 1/16

Therefore, the probability that at least one of the events occurs, is

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