Multiple choice

One ticket is drawn from a bag containing 70 tickets numbered 1 to 70 Find the probability that it is a multiple of 5 or 7

  1. $1/10$
  2. $1/70$
  3. $6/70$
  4. $11/35$
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D Correct answer
Explanation

Multiples of 5: 70/5 = 14. Multiples of 7: 70/7 = 10. Multiples of both (35): 70/35 = 2. Total favorable = 14 + 10 - 2 = 22. Probability = 22/70 = 11/35.

AI explanation

Among the numbers from 1 to 70, there are 14 multiples of 5 and 10 multiples of 7. We must subtract the common multiples of both 5 and 7, which are the multiples of 35 (specifically 35 and 70), leaving exactly 2 numbers. Using the addition theorem of probability for mutually exclusive counting, the total favorable numbers are 14 plus 10 minus 2, equaling 22. The required probability is 22 divided by 70, which simplifies to 11 divided by 35.

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