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Problem 197

Number theory Difficulty 1.5 Multiple choice CEMC Gauss (Grade 7) · Canada · 2020

A box contains 15 red, 20 blue, and 16 green jelly beans. Jack first chooses a green jelly bean and eats it. Then he chooses a blue jelly bean and eats it. If each of the remaining jelly beans is equally likely to be chosen, what is the probability that Jack chooses a red jelly bean next?

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Official solution

Before Jack eats any jelly beans, the box contains 15+20+16=5115+20+16=51 jelly beans.

After Jack eats 2 jelly beans, there are 512=4951-2=49 jelly beans remaining in the box.

One of the jelly beans that Jack ate was green, and the other was blue.

Thus after eating the 2 jelly beans, there are still 15 red jelly beans in the box.
If each of the remaining jelly beans is equally likely to be chosen, the probability that Jack chooses a red jelly bean next is 1549\frac{15}{49}.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.