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Probability

Question
CBSEENMA12033706

Fatima and John appear in an interview for two vacancies in the same post. The probability of Fatima's selection is 1 over 7 space and spacethat of John's selection is 1 fifth. What is the probability that none of them will be selected.

Solution

P(none of them will be selected)
                                     = P(not A and not B)
                                     = P(not A). P(not B)
                                     = [1 - P(A)] [1 - P(B)]
                                     =open square brackets 1 minus 1 over 7 close square brackets space open square brackets 1 minus 1 fifth close square brackets space equals space 6 over 7 cross times 4 over 5 space equals space 24 over 35

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