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A bouquet of 3 flowers is to be made from 3 roses and 2 lilies. What is the probability that the bouquet has at least one lily?

A bouquet of 3 flowers is to be made from 3 roses and 2 lilies. What is the probability that the bouquet has at least one lily? Correct Answer 9/10

Total number of flowers = 3 + 2 = 5

Let S be the sample space. Then,

n(S) = total number of ways of selecting 3 flowers out of 5 = ⁵C₃ = (5 × 4 × 3!) / (3! × 2 × 1) = 10

Let E= event of selecting 3 flowers when none is a lily n(E) = 3C3 = 1

∴ P (E) when none of the flowers is a lily = 1/10

∴ P (E) when at least one flower is a lily = 1 – 1/10 = 9/10

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