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OlympiadBench / 2343 / A bag contains 40 balls, each of which is black or gold. Feridun reaches into…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

answer type

Numerical

is multiple answer

false

language

English

question

A bag contains 40 balls, each of which is black or gold. Feridun reaches into the bag and randomly removes two balls. Each ball in the bag is equally likely to be removed. If the probability that two gold balls are removed is

\frac{5}{12}

, how many of the 40 balls are gold?

Plain-text mathematical notation (without MathML)

A bag contains 40 balls, each of which is black or gold. Feridun reaches into the bag and randomly removes two balls. Each ball in the bag is equally likely to be removed. If the probability that two gold balls are removed is (5)/(12), how many of the 40 balls are gold?

Original LaTeX notation

A bag contains 40 balls, each of which is black or gold. Feridun reaches into the bag and randomly removes two balls. Each ball in the bag is equally likely to be removed. If the probability that two gold balls are removed is $\frac{5}{12}$, how many of the 40 balls are gold?

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2343
task_id: 0649ffd5-6852-5f59-8df3-03ea41f09793
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2343
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import