Question
A basket contains 3 yellow, 5 purple and 3 red
flowers. If 3 flowers are drawn at random, what is the probability that at least two are of same colour?Solution
Total number of flowers = 3 + 5 + 8 = 11 Let S be the sample space. Then, n(S) = number of ways of drawing 3 flowers out of 11 = ¹¹C₃ = (11 × 10 × 9)/(3 × 2 × 1) = 165 Let E= event of drawing 3 flowers none is of same colour = n(E) = ³C_1 × ⁵C_1 × ³C_1 = 3 × 5 × 3 = 45 ∴ P (E) = (n(E))/(n(S)) = 45/165 = 9/33 ∴ Event of drawing 3 flowers when at least 2 are of same colour = 1 - 9/33 = 8/11
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