Q41 of 43 Page 15

In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7. The probability of passing atleast one of them is 0.95. What is the probability of passing both?


Let E, F denote the events that a student passes the first and second examinations, respectively.

We have, P(E) = 0.8

P(F) = 0.7

P(E or F) = P(E ∪ F) = 0.95

Therefore, P(E ∪ F) = P(E) + P(F) - P(E ∩ F ) ⇒ 0.95 = 0.8 +0.7 – P(E ∩ F)

P(E ∩ F) = 0.55

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