Question

From $X=\{1,2,\cdots 25\}$ a number is selected randomly from $X$ and found to be prime. The probability that it is more than $12$ is

• A. $\frac{9}{25}$
• B. $\frac{4}{9}$
• C. $\frac{4}{25}$
• D. None of these

Answer 1

The correct option is C $\frac{4}{25}$

$n\left(S\right)=25$
$n\left(A\right)=$ total prime number $=9$
$n\left(B\right)=$prime number $>12=4$
$\therefore$ Required probability $=$ Probability of a prime $\times$ Probability of
drawing more than $10$ from the prime number.
$=\frac{9}{25}\times \frac{4}{9}=\frac{4}{25}$