Question

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?

Class X1 - Maths -Probability Page 405

Answer 1

Given,
Probability of passing the 1st examination = 0.8
e.g P( 1st) = 0.8
Probability of passing the 2nd examination = 0.7
e.g P(2nd ) = 0.7
Probability of passing at least one of them = 0.95
e.g P( 1st U 2nd ) = 0.95
P( Probability of passing both ) = P( 1st ∩ 2nd)

use formula ,
P(A U B) = P(A ) + P(B ) - P(A ∩ B)
P( 1st U 2nd ) = P(1st ) + P(2nd ) - P( 1st ∩ 2nd)
0.95 = 0.8 + 0.7 - P( 1st ∩ 2nd)
P( 1st ∩ 2nd) = 0.55

Answer 2

Let A and B be the events of passing first and 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 = 0.55

Thus, the probability of passing both examinations is 0.55.

I HOPE IT WILL HELP YOU.

THANK YOU.