Let A and B be the events of passing English and Hindi examinations, respectively.
Accordingly, we have:
P(A and B) = 0.5
P(not A and not B) = 0.1 [i.e. P(A' ∩ B') = 0.1]
P(A) = 0.75
Now, P(A∪B) + P(A' ∩ B') = 1
⇒ P(A∪B) = 1 P(A' ∩ B')
= 1 0.1 = 0.9
By addition theorem, we have:
P(A ∪ B) = P(A) + P(B) P(A ∩ B)
⇒ 0.9 = 0.75 + P (B) 0.5
⇒ P(B) = 0.9 0.75 + 0.5
⇒ P(B) = 0.65
Thus, the probability of passing the Hindi examination is 0.65.