Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

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 - Mathematics

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 the second examinations, respectively.
Accordingly, P(A) = 0.8, P(B) = 0.7 and P(A or B) = 0.95
We know that
P(A or B) = P(A) + P(B) – P(A and B)
⇒ 0.95 = 0.8 + 0.7 – P(A and B)
⇒ P(A and B) = 0.8 + 0.7 – 0.95
= 1.5 - 0.95 = 0.55
Thus, the probability of passing both the examinations is 0.55.

Concept: Probability - Probability of 'Not', 'And' and 'Or' Events
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.4 | Q 21 | Page 69