Multiple choice

A bag contains balls numbered from 1 to 30 and a ball is picked at random from it. What is the probability that the ball picked has a number which is a multiple of 3 or 5, but not of both 3 and 5?

  1. 2/5

  2. 8/15

  3. 7/15

  4. 1/3

  5. 1/5
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A Correct answer
Explanation

Multiples of 3: 10. Multiples of 5: 6. Multiples of both (15): 2. Multiples of 3 or 5 but not both = (10-2) + (6-2) = 8 + 4 = 12. Probability = 12/30 = 2/5.

AI explanation

Using the principle of sets, we first find the multiples of 3 up to 30, which gives 10 numbers, and the multiples of 5 up to 30, which gives 6 numbers. The multiples of both 3 and 5 are the multiples of 15, which gives the numbers 15 and 30, totaling 2 numbers. We subtract the multiples of 15 from the total of the individual sets to find the numbers that are multiples of 3 or 5 but not both, giving 10 plus 6 minus 4, which equals 12. The probability is 12 favorable outcomes divided by 30 total outcomes, simplifying to the result of 2 over 5.

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