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Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?

Correct answer: D. 5/6Pakistan Studies Quiz

  • A. 1/6
  • B. 5/8
  • C. 3/8
  • D. 5/6Pakistan Studies Quiz

Explanation

Use the complement: the probability of selecting no graduate is C(6,3) ÷ C(10,3) = 20 ÷ 120 = 1/6, because 6 of the 10 people are non-graduates. Hence the probability of at least one graduate is 1 - 1/6 = 5/6. Students may choose 1/6 by reporting the probability of no graduate instead of its complement.

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