Multiple choice

One lottery ticket is drawn at random from a bag containing $20$ tickets numbered from $1$ to $20$. Find the probability that the number drawn is divisible by $3$ or $5$:

  1. $\displaystyle \frac{6}{20}$
  2. $\displaystyle \frac{7}{20}$
  3. $\displaystyle \frac{8}{20}$
  4. $\displaystyle \frac{9}{20}$
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D Correct answer
Explanation

Numbers divisible by 3 are {3, 6, 9, 12, 15, 18} (6 numbers). Numbers divisible by 5 are {5, 10, 15, 20} (4 numbers). The number 15 is counted in both, so the unique numbers are {3, 5, 6, 9, 10, 12, 15, 18, 20}, which is 9 total. The probability is 9/20.

AI explanation

By the set theory formula for probability, we calculate P(A union B) = P(A) + P(B) - P(A intersection B). The multiples of 3 are 3, 6, 9, 12, 15, 18 (6 numbers), the multiples of 5 are 5, 10, 15, 20 (4 numbers), and 15 is the only multiple of both. The total favorable outcomes are 6 + 4 - 1 = 9, making the probability 9/20.

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