At least one ripe fruit in the basket pick

Question

A basket holds 15 fruits, of which 5 are ripe and 10 are unripe. You pick 4 fruits at random. What is the probability that at least one of your 4 fruits is ripe?

Accepted Answer

"At least one ripe" bundles several cases, so flip it: find the chance of "no ripe fruit" and subtract from 1. Chance of zero ripe means all 4 come from the 10 unripe fruits. With combinations, where \binom{n}{k} counts ways to choose k from n: P(	ext{none ripe})=\frac{\binom{10}{4}}{\binom{15}{4}}=\frac{210}{1365}=\frac{2}{13}. Subtract from 1: 1-\frac{2}{13}=\frac{11}{13}\approx 0.846. Takeaway. The more items you pick, the smaller the "none of the good ones" chance becomes, so "at least one" climbs toward certainty. The complement rule keeps the computation to a single fraction.

At least one ripe fruit in the basket pick

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