Question

24 cards numbered 1, 2, 3, ...., 23, 24 are put in a box and mixed thoroughly. One person draws a card from the box. The probability that the number on the card is divisible by 2 or 3 or both is

• A. $\frac{1}{6}$
• B. $\frac{5}{6}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

The correct option is D $\frac{2}{3}$

The total possible outcomes = 24

Numbers divisible by only 2 are 2 ,4, 8 , 10, 14,16,20 ,22 ( 8 numbers) ---------(1)

Numbers divisible only by 3 are 3, 9 , 15 , 21 ( 4 numbers) ---------(2)

Numbers divisible by both 2 and 3 are 6,12,18, 24 ( 4 numbers) ---------(3)

From (1),(2) and (3), we see that the number of favourable outcomes is 16 (i.e.,8 + 4 + 4).
We know that, Probability of an event E, P(E) =$\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$
$\therefore \text{Probablity}=\frac{16}{24}$
$=\frac{2}{3}$