# Answer to Question #23927 in Statistics and Probability for umesh jha

Question #23927

the probability that a candidate passes in physics is 70% and that he passes in chemistry is 40%. What is the probability that the candidate passes in any one of the two subjects?

Expert's answer

The probability that the candidate passes both of the two subjects is

P(both) = 0.7·0.4 = 0.28.

The probability that the candidate passes none of the two subjects is

P(none) = (1-0.7)·(1-0.4) = 0.3·0.6 = 0.18.

Therefore, the probability that the candidate passes in any one of the two subjects is

P(any) = 1 - P(both) - P(none) = 1 - 0.28 - 0.18 = 0.54.

P(both) = 0.7·0.4 = 0.28.

The probability that the candidate passes none of the two subjects is

P(none) = (1-0.7)·(1-0.4) = 0.3·0.6 = 0.18.

Therefore, the probability that the candidate passes in any one of the two subjects is

P(any) = 1 - P(both) - P(none) = 1 - 0.28 - 0.18 = 0.54.

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