Multiple choice

From a set of 17 cards numbered 1 to 17, one card is drawn at random. What is the probability that the number is divisible by 3 or 7?

  1. 3 17

  2. 5 17

  3. 6 17

  4. 7 17
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D Correct answer
Explanation

Numbers divisible by 3: 3, 6, 9, 12, 15 (5 numbers). Numbers divisible by 7: 7, 14 (2 numbers). No overlap. Total = 7 numbers. Probability = 7/17.

AI explanation

Using the addition theorem of probability, the probability of drawing a number divisible by 3 or 7 is P(A) plus P(B) minus P(A intersection B). The numbers divisible by 3 are 3, 6, 9, 12 and 15, while those divisible by 7 are 7 and 14, with no overlap. This gives 7 favorable outcomes out of 17 total cards, so the probability is 7/17.

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