# 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?

**Solution:**

Let A and B be the events of passing the English and Hindi examinations respectively.

Then the given probabilities are,

P (A) = 0.75, P (A ∩ B) = 0.5, P (not A and not B) = P ( A' ∩ B') = 0.1.

By De Morgan’s law,

(A' ∩ B') = (A υ B)'

Therfore,

P (A' ∩ B') = P (A υ B)' = 0.1

Now,

P (A υ B) = 1 - P (A υ B)'

= 1 - 0.1

= 0.9

Using P (A υ B) formula,

P (A υ B) = P (A) + P (B) - P (A ∩ B)

P (B) = P (A υ B) - P (A) + P (A ∩ B)

= 0.9 - 0.75 + 0.5

= 0.65

Thus, the probability of passing the Hindi examination is 0.65

NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.3 Question 20

## 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?

**Summary:**

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, then the probability of passing the Hindi examination is 0.65