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Unit 1 · Discrete Structures and Optimisation Paper 2 CS · June 2024 Re-Exam

Match List I (Queries) with List II (Probability)
List IList II
(A) A bag contains 6 white and 4 red balls. Two balls are drawn at random. What is the chance they will be the same colour?(I) 3/68
(B) In a pack of 52 cards, one card is drawn at random. What is the probability that it is either a king or a queen?(II) 14/68
(C) A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability of 1 red and 2 white balls.(III) 2/13
(D) A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability of 2 blue and 1 red ball.(IV) 7/15

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Correct answer: D. (A)-(IV), (B)-(III), (C)-(I), (D)-(II)

Explanation

(A) [C(6,2) + C(4,2)] / C(10,2) = (15 + 6)/45 = 7/15 → IV. (B) 8/52 = 2/13 → III. (C) C(6,1)·C(4,2)/C(18,3) = 36/816 = 3/68 → I. (D) C(8,2)·C(6,1)/C(18,3) = 168/816 = 14/68 → II.

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