Track / Stage 4 / 236 of 340 #496 of 1964

Problem 496

AMC 12 late, AIME early

Combinatorics Difficulty 4.9 Multiple choice

A bottle of children's vitamins contains tablets in three different shapes. Among the vitamins, there are 60 squares, 60 triangles and 60 stars. Each shape comes in an equal number of three different flavours - strawberry, grape and orange. A tablet is randomly chosen from a newly opened bottle. What is the probability that this tablet is a grape star?

Pick one

Official solution

In the bottle, there are a total of 180 tablets.

Among the 60 stars, there are an equal number of each of the three flavours - strawberry, grape and orange. This tells us that there are 20 grape stars.

If each tablet is equally likely to be chosen from the bottle, the probability of choosing a grape star is

$\frac{\text { Number of grape stars }}{\text { Total number of tablets }}=\frac{20}{180}=\frac{1}{9}$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.