Multiple choice

$17$ cards are numbered $1,2,3.... 16,17$ are put in a box and mixed. A card is drawn at random from the box. What is the probability that the card is divisible by both $2$ & $3$?

  1. $\dfrac{1}{17}$
  2. $\dfrac{2}{17}$
  3. $\dfrac{3}{17}$
  4. $\dfrac{4}{17}$
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B Correct answer
Explanation

Numbers divisible by both 2 and 3 must be divisible by 6. In the range 1 to 17, these are 6 and 12. There are 2 such numbers. Probability = 2/17.

AI explanation

For a number to be divisible by both 2 and 3, it must be divisible by their least common multiple, which is 6. From the numbers 1 through 17, the numbers divisible by 6 are 6 and 12, yielding 2 favorable outcomes. Since the total number of possible outcomes is 17, the probability is 2 divided by 17.

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