Question

In a committee of $25$ member, each member is proficient either in Mathematics or in satists or in both. If $19$ of these are profiicint in mathematics, $16$ in statistics, find the probability that a person selected from the committee is proficient in both.

Answer 1

Let proficient in mathematics be event $A$ and that in statistics be $B$.

then $n\left(A\right)=19$ and $P\left(B\right)=16$

Now, $n(A\cup B)=25$

We know,

$n(A\cup B)=n\left(A\right)+P\left(B\right)-n(A\cap B)$

or , $25=19+16-n(A\cap B)$

$\therefore n(A\cap B)=10$

$\therefore$ Probability of a person selected from the committee is proficient in both is $\frac{10}{25}=\frac{2}{5}$ Ans