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 ?

Vedclass pdf generator app on play store
Vedclass iOS app on app store

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 $0.55$.

Similar Questions

$A$ and $B$ are events such that $P(A)=0.42$,  $P(B)=0.48$ and $P(A$ and $B)=0.16 .$ Determine $P (A$ or $B).$

In a hostel, $60 \%$ of the students read Hindi newspaper, $40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. A student is selected at random Find the probability that she reads neither Hindi nor English newspapers.

If from each of the three boxes containing $3$ white and $1$ black, $2$ white and $2$ black, $1$ white and $3$ black balls, one ball is drawn at random, then the probability that $2$ white and $1$ black ball will be drawn is

  • [IIT 1998]

Let $X$ and $Y$ are two events such that $P(X \cup Y=P)\,(X \cap Y).$

Statement $1:$ $P(X \cap Y' = P)\,(X' \cap Y = 0).$

Statement $2:$ $P(X) + P(Y = 2)\,P\,(X \cap Y)$

  • [AIEEE 2012]

Given $P(A)=\frac{3}{5}$ and $P(B)=\frac{1}{5}$. Find $P(A $  or  $B),$ if $A$ and $B$ are mutually exclusive events.