Given,
24 cards numbered 1, 2, 3, ...., 23, 24
Here, the total possible outcomes = 24
Numbers divisible by only 2 are 2, 4, 8, 10, 14, 16, 20, 22
∴ 8 numbers are divisible by only 2 ...(i)
Numbers divisible by only 3 are 3, 9, 15, 21
∴ 4 numbers are divisible by only 3 ...(ii)
Numbers divisible by both 2 and 3 are 6, 12, 18, 24
∴ 4 numbers are divisible by both 2 and 3 ...(iii)
From (i),(ii) and (iii), we get
The number of favourable outcomes = 8 + 4 + 4 = 16
We know that, Probability of an event E is given by,
P(E) =Number of favourable outcomesTotal number of outcomes
⇒ P(E)= 1624
=23
∴ The probability that the number on the card is divisible by 2 or 3 or both is 23