Track / Stage 4 / 312 of 340 #572 of 1964

Problem 572

AMC 12 late, AIME early

Combinatorics Difficulty 5.0 Find the answer

2. A box contains $m$ red balls, 10 white balls, and $n$ black balls. Each ball is identical except for its color. If a ball is randomly drawn from the box, the probability of drawing a white ball is the same as the probability of not drawing a white ball. What is the relationship between $m$ and $n$ ? (:

Pick one

Official solution

2. A.

The total number of balls in the box is $m+n+10$ , the probability of drawing a white ball is $P=\frac{10}{m+n+10}$ ; the probability of not drawing a white ball is $P^{\prime}=\frac{m+n}{m+n+10}$ .
According to the problem, $\frac{10}{m+n+10}=\frac{m+n}{m+n+10}$ . Therefore, $m+n=10$ .

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