In an entrance test that is graded on basis of two examinations, probability of a randomly chosen st

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14.Probability

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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 ?

A

$0.55$

B

$0.55$

C

$0.55$

D

$0.55$

Solution

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 the examinations is $0.55$.

Standard 11

Mathematics

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(IIT-1988)