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Grand Oral Maths with Questions and Answers
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Grand Oral Maths with Questions and Answers A man draws a single card from a standard 52-card deck. What is the probability that the card is either a heart or a face card (Jack, Queen, King)? Working: Let H = hearts, F = face cards. |H| = 13 |F| = 12 (J, Q, K of 4 suits = 12 cards) Intersection H ∩ F = 3 (J♥, Q♥, K♥) Using inclusion–exclusion: P(H ∪ F) = (13 + 12 − 3) / 52 = 22 / 52 = 11 / 26 Correct Answer: 11/26 A factory produces items with a 3% defect rate. If 5 items are selected at random, what is the probability that exactly one is defective? Working: This follows a binomial distribution: n = 5, p = 0.03, q = 0.97 P(X = 1) = C(5,1)(0.03)(0.97)^4 C(5,1) = 5 (0.97)^4 ≈ 0. P = 5 × 0.03 × 0. P ≈ 0.1327939 Correct Answer: ≈ 0.1328
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