Question

From a pack of $100$ cards numbered $1$ to $100,$ a card is choosen at random. Then the probability that the number obtained on the card is divisible by $4$ or $5$ is

• A. $\frac{9}{20}$
• B. $\frac{3}{10}$
• C. $\frac{2}{5}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{2}{5}$

Let event $A=$ number obtained on the card is divisible by $4$
$B=$ number obtained on the card is divisible by $5$
$A\cap B=$ number obtained is divisible by both, i.e. divisible by $20.$
$\Rightarrow P\left(A\right)=\frac{25}{100},P\left(B\right)=\frac{20}{100},P(A\cap B)=\frac{5}{100}$
So, Required probability :
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)=\frac{40}{100}=\frac{2}{5}$