# Difference between revisions of "1994 AHSME Problems/Problem 27"

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<math> \textbf{(A)}\ \frac{1}{2} \qquad\textbf{(B)}\ \frac{5}{9} \qquad\textbf{(C)}\ \frac{4}{7} \qquad\textbf{(D)}\ \frac{3}{5} \qquad\textbf{(E)}\ \frac{2}{3} </math> | <math> \textbf{(A)}\ \frac{1}{2} \qquad\textbf{(B)}\ \frac{5}{9} \qquad\textbf{(C)}\ \frac{4}{7} \qquad\textbf{(D)}\ \frac{3}{5} \qquad\textbf{(E)}\ \frac{2}{3} </math> | ||

==Solution== | ==Solution== | ||

+ | To find the probability that the kernel is white, the probability of <math>P(white|popped) = \frac{P(white, popped)}{P(popped)}</math> | ||

+ | |||

+ | Running a bit of calculations <math>P(white, popped) = \frac{1}{3}</math> while <math>P(popped) = \frac{1}{3} + \frac{2}{9} = \frac{5}{9}</math> Plugging this into the earlier equation, <math>P(white|popped) = \frac{\frac{1}{3}}{\frac{5}{9}}</math>. Meaning that the answer is <math>\boxed{\textbf{(D)}\ \frac{3}{5}}</math>. |

## Revision as of 20:04, 14 February 2017

## Problem

A bag of popping corn contains white kernels and yellow kernels. Only of the white kernels will pop, whereas of the yellow ones will pop. A kernel is selected at random from the bag, and pops when placed in the popper. What is the probability that the kernel selected was white?

## Solution

To find the probability that the kernel is white, the probability of

Running a bit of calculations while Plugging this into the earlier equation, . Meaning that the answer is .