Multiple choice

There are 30 cards of same size in a bag on which numbers 1 to 30 are written. One card is taken out of the bag at random. Find the probability that the number on the selected card is not divisible by 3.

  1. $\dfrac{5}{6}$
  2. $\dfrac{2}{3}$
  3. $\dfrac{1}{3}$

  4. None of these
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B Correct answer
Explanation

Numbers divisible by 3 from 1 to 30 are 3, 6, ..., 30 (10 numbers). Numbers not divisible by 3 = 30 - 10 = 20. Probability = 20/30 = 2/3.

AI explanation

From the numbers 1 to 30, there are exactly 10 numbers divisible by 3 (3, 6, 9, 12, 15, 18, 21, 24, 27, 30). This means there are 30 minus 10, or 20 numbers that are not divisible by 3. The probability of selecting a number not divisible by 3 is the number of such outcomes divided by the total outcomes, which is 20 / 30, simplifying to 2 / 3.

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