Q42 of 43 Page 15

The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Hindi examination?


Let E, F denote the events that a student will pass English and Hindi respectively.

Thus, P(E) = 0.75

P(E ∩ F) = 0.5

and P(E ∪ F)’ = 0.1

or 1 - P(E ∪ F) = 0.1

or P(E ∪ F) = 1 – 0.1 = 0.9

Hence, P(E ∪ F) = P(E) + P(F) – P(E ∩ F)

or 0.9 = 0.75 + P(F) – 0.5
or P(F) = 0.65.

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