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 at least one of them is 0.95. What is the probability of passing both?

Solution:

Let A and B be the events of passing the first and second examinations respectively.

Accordingly, P (A) = 0.8, P (B) = 0.7 and P (A or B) = 0.95

Using P(A or B) formula,

P (A or B) = P (A) + P (B) - P (A and B)

0.95 = 0.8 + 0.7 - P (A and B)

0.95 = 1.5 - P (A and B)

P (A and B) = 1.5 - 0.95 = 0.55

Thus, the probability of passing both examinations is 0.55

NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.3 Question 19

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 at least one of them is 0.95. What is the probability of passing both?

Summary:

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 at least one of them is 0.95. Then the probability of passing both examinations is 0.55