Multiple choice

A box contains $20$ balls bearing numbers, $1,2,3,4, ....., 20$. A ball is drawn at random from the box. What is the probability that the number on the ball is divisible by $2$ or $3$.

  1. $\dfrac{6}{10}$
  2. $\dfrac{11}{20}$
  3. $\dfrac{13}{20}$

  4. None of these
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C Correct answer
Explanation

Numbers divisible by 2: 10. Numbers divisible by 3: 6 (3, 6, 9, 12, 15, 18). Numbers divisible by both (6): 3 (6, 12, 18). Using inclusion-exclusion: 10 + 6 - 3 = 13. Probability = 13/20.

AI explanation

The total number of possible outcomes when drawing one ball from 20 is 20. The numbers divisible by 2 or 3 are calculated using the addition theorem of probability as P(2) plus P(3) minus P(6). This gives 10/20 plus 6/20 minus 3/20, which equals 13/20.

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