Competition problem — Combinatorics

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Combinatorics Difficulty 2.3 Junior Find the answer

A box contains $5$ chips, numbered $1$ , $2$ , $3$ , $4$ , and $5$ . Chips are drawn randomly one at a time without replacement until the sum of the values drawn exceeds $4$ . What is the probability that $3$ draws are required?

Pick one

Solution

Notice that the only four ways such that $3$ draws are required are $1,2$ ; $1,3$ ; $2,1$ ; and $3,1$ . Notice that each of those cases has a $\frac{1}{5} \cdot \frac{1}{4}$ chance, so the answer is $\frac{1}{5} \cdot \frac{1}{4} \cdot 4 = \frac{1}{5}$ , or $\boxed{D}$ .
Jonathan Xu (pi_is_delicious_69420)

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.