Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

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?

Advertisement Remove all ads


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
  Is there an error in this question or solution?
Advertisement Remove all ads


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

View all notifications

      Forgot password?
View in app×