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NDA 2024 Maths · Mathematics · Probability · medium

A number is selected at random from the integers 1 to 30. The probability that it is a multiple of 3 or of 5 is

Single correct option

A number is selected at random from the integers 11 to 3030. The probability that it is a multiple of 33 or of 55 is
  1. A. 815\frac{8}{15}
  2. B. 12\frac12
  3. C. 25\frac25
  4. D. 715\frac{7}{15}
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Answer: (D) 715\frac{7}{15}

Multiples of 3: 10; of 5: 6; of both (multiples of 15): 2. By inclusion-exclusion, 10+6−2=1410+6-2=14 numbers, so the probability is 1430=715\frac{14}{30}=\frac7{15}. Trap: 1630=815\frac{16}{30}=\frac8{15} forgets to subtract the overlap, and 25\frac25 counts only multiples of 3 and 5 separately-incomplete.
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Original question written in the NDA 2024 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake