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Question -

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?



Answer -

Let us assume probability of passing the English examinationis 0.75 be P(A).

And also assume the probability of passing the Hindiexamination is be P(B).

Here given, P(A) = 0.75, P(A∩B) – 0.5, P(AI∩BI)= 0.1

We know that, P(AI∩BI) = 1 – P(A∪B)

Then, P(A∪B) = 1 – P(AI∩BI)

= 1 – 0.1

= 0.9

∴ P(A∪B) = P(A) + P(B) – P(A∩B)

0.9 = 0.75 + P(B) – 0.5

Transposing 0.75, – 0.5 to LHS and it becomes – 0.75, 0.5.

P(B) = 0.9 + 0.5 – 0.75

= 0.65

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