SOLUTION: the probability is 2/3 that MR.A will pass the exams and the probability is 3/4 that MR B will pass the exams . find the probability tha some body will pass the exams

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Question 1163880: the probability is 2/3 that MR.A will pass the exams and the probability is 3/4 that MR B will pass the exams . find the probability tha some body will pass the exams
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
p(A) = 2/3
p(B) = 3/4
probability that somebody will pass the exams is equal to 1 minus th probability that nobody will pass the exams.
probability that nobody passes the exams is equal to 1/3 * 1/4 = 1/12.
the probability that somebody passes the exams is therefore 1 - 1/12 = 11/12.

another formula you can use on this problem is p(A or B) = p(A) + p(B) - p(A and B)
that formula becomes 2/3 + 3/4 - 2/3 * 3/4 which becomes 2/3 + 3/4 - 6/12 which becomes 8/12 + 9/12 - 6/12 which becomes 17/12 - 6/12 which becomes 11/12.

the full probabilities are:

p(A and B) = 2/3 * 3/4 = 6/12
p(A) and not p(B) = 2/3 * 1/4 = 2/12
not p(A) and p(B) = 1/3 * 3/4 = 3/12
not p(A) and not p(B) = 1/3 * 1/4 = 1/12

the total probabilities are (6 + 2 + 3 + 1) / 12 = 12/12 = 1, as they should be.