Multiple choice

In a set of 24 cards, each card is numbered with a different positive integer from 1 to 24. One card will be drawn at random from the set. What is the probability that the card drawn will have either a number that is divisible by both 2 and 3 or a number that is divisible by 7 ?

  1. 3/24

  2. 4/24

  3. 7/24

  4. 8/24

  5. 17/24
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C Correct answer
Explanation

Divisible by 2 and 3 (i.e., by 6): 6, 12, 18, 24 (4 numbers). Divisible by 7: 7, 14, 21 (3 numbers). Total unique numbers = 4 + 3 = 7. Probability = 7/24.

AI explanation

To find the probability, we count the integers from 1 to 24 that are divisible by both 2 and 3, or by 7. The numbers divisible by both 2 and 3 are multiples of 6, which are 6, 12, 18, and 24. The numbers divisible by 7 are 7, 14, and 21. This gives a total of 7 favorable outcomes out of 24 possible outcomes, so the probability is 7/24.

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