Multiple choice

From a set of $17$ cards numbered $1$ to $17$ one is drawn at random. The probability that it is divisible by $3$ or $5$ is

  1. $\dfrac{8}{17}$
  2. $\dfrac{5}{17}$
  3. $\dfrac{6}{17}$
  4. $\dfrac{7}{17}$
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D Correct answer
Explanation

Numbers divisible by 3: 3, 6, 9, 12, 15 (5 numbers). Numbers divisible by 5: 5, 10, 15 (3 numbers). The number 15 is counted twice. Total unique numbers = 5 + 3 - 1 = 7. Probability = 7/17.

AI explanation

Using the addition theorem of probability for the union of two events, we calculate the favorable outcomes as the sum of multiples of 3 (which are 3, 6, 9, 12, 15) and multiples of 5 (5, 10, 15), minus the common multiple 15 to avoid double counting. This gives 5 + 3 - 1 = 7 favorable cards out of 17 total cards. The required probability is 7/17.

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