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
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) =number of favourable outcomestotal number of outcomes
∴Probablity=1624
=23