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?

Explanation

Let A: student passes in English.
B: Student passes in Hindi
Given: P(A) = 0.75, P(A∩B) = 0.5 and P (neither A nor B) = P((A ∪ B)’) = 0.1
To find:
P(B) Now, P((A∪B)’) = 1- P(A∪B)
⇒ 0.1=1 – P(A∪B) ∵ P((A∪B)’) = 0.1
∴ P{A ∪ B) = 1- 01 = 0.9
P(A) + P(B) – P(A ∩ B) = 0. 9
∴ 0.75 + P(B) – 0.5 = 0.9
∴ P(B) = 1.4 – 0.75 = 0.65