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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
13
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B

16

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C
23
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D

56

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Solution

The correct option is C 23

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


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