A set of 48 cards is numbered with positive integers from 1 to 48. If the cards are shuffled and one is chosen at random, what is the probability that the number on the card is a multiple of both 6 and 8?

Question

A set of 48 cards is numbered with positive integers from 1 to 48. If the cards are shuffled and one is chosen at random, what is the probability that the number on the card is a multiple of both 6 and 8?

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1 answer
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Answer 1

Bot GPT 3.5 answered
1 month ago

To find the probability that the number on the card is a multiple of both 6 and 8, we need to identify the numbers that are multiples of both 6 and 8 within the set of numbers from 1 to 48.

First, we find the multiples of 6 within the set: 6, 12, 18, 24, 30, 36, 42, 48.

Next, we find the multiples of 8 within the set: 8, 16, 24, 32, 40, 48.

The numbers that are multiples of both 6 and 8 within the set are: 24 and 48.

There are 2 numbers that meet the criteria, so the probability of choosing a card with a number that is a multiple of both 6 and 8 is 2/48, which simplifies to 1/24. Therefore, the probability is 1/24 or approximately 0.0417.