Question

A number is selected from the first 25 natural numbers. What is the probability that it would be divisible by 4 or 7 ?

• A. $\frac{1}{25}$
• B. $\frac{9}{25}$
• C. $\frac{9}{14}$
• D. $\frac{6}{11}$

Answer 1

The correct option is B $\frac{9}{25}$

Let A be the event that the number selected would be divisible by 4.
B be the event that the selected number would be divisible by 7.
Then, $A\cup B$ denotes the event that the number would be divisible by 4 or 7.
Sample space $S=\{1,2,3,\mathrm{4....25}\}$
$A=\{4,8,12,16,20,24\}$
$B=\{7,14,21\}$
Since $A\cap B$ is a null set , A and B are mutually exclusive.
$P(A\cup B)=P\left(A\right)+P\left(B\right)P(A\cup B)=\frac{6}{25}+\frac{3}{25}=\frac{9}{25}$