Question

From a set of 100 cards numbered 1 to 100, one card is drawn at random. The probability that the number obtained on the card is divisible by 6 or 8 but not by 24, is

• A. $\frac{6}{25}$
• B. $\frac{1}{4}$
• C. $\frac{1}{5}$
• D. $\frac{2}{5}$

Answer 1

The correct option is C $\frac{1}{5}$

From given, we have,

$6,8$ have LCM $24$

Therefore, any number divisible by both $6,8$ is also divisible by $24$

There are $4$ numbers divisible by $24$ from $1$ to $100$

There are $16$ numbers multiple of $6$ from $1$ to $100$

There are $12$ numbers multiple of $8$ from $1$ to $100$

The number of numbers obtained on the card is divisible by 6 or 8

$=16+12-4=24$

The number of numbers obtained on the card is divisible by 6 or 8 but not by 24

$=24-4=20$

Required probability

$P=\frac{20}{100}=\frac{1}{5}$