Theory question 113
ProbabilityAn association is made up of 10 journalists and 9 engineers. If a committee of 4 members is to be formed from the association, find the probability that it will consist of: (a) at least two engineers; (b) 75% journalists; (c) odd number of engineers.
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Model answer
Total committees: ¹⁹C₄ = 3876.
(a) 2E: ⁹C₂ × ¹⁰C₂ = 1620; 3E: ⁹C₃ × ¹⁰C₁ = 840; 4E: ⁹C₄ = 126. P = 2586/3876 = 431/646 ≈ 0.667.
(b) 3 journalists and 1 engineer: ¹⁰C₃ × 9 = 1080. P = 1080/3876 = 90/323 ≈ 0.279.
(c) 1E: 1080; 3E: 840. P = 1920/3876 = 160/323 ≈ 0.495.
Explanation
Count the favourable committees, then divide by ¹⁹C₄.