Discussion
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
Answer: B
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 outcomes/ total number of outcomes
=16/24
=2/3
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