Question

A basket contains 3 yellow, 5 purple and 3 red flowers. If 3 flowers are drawn at random, what is the probability that all are purple?

A 4/33 Correct Answer Incorrect Answer
B 1/33 Correct Answer Incorrect Answer
C 1/55 Correct Answer Incorrect Answer
D 2/33 Correct Answer Incorrect Answer
E None of these Correct Answer Incorrect Answer

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 all the flowers are of purple colour n(E) = ⁵C_3 = (5 × 4)/2 = 10 ∴ P (E) = (n(E))/(n(S)) = 10/165 = 2/33

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