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> | ||
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| + | 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 19:04, 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 
.
