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?
Answer Choices:
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Solution:
Let the total number of kernels be , so that there are white kernels and yellow kernels. Then of the kernels will pop ( white and yellow). Hence the probability that the popped kernel was white is .
Make a probability tree diagram:
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Since of the kernels popped and of the kernels are white and popped, the probability that the popped kernel was white is .
Make a diagram as indicated, letting areas represent the probabilities. The ratio of the area shaded with line segments to the area shaded with segments or dots is
Note. This is an application of Bayes' Theorem.
Use a Venn diagram where the universal set is the set of kernels, is the set of white kernels, and is the set of kernels which will pop. Let be the number of kernels in and , and let be the number of kernels not in . Then there are kernels in . Thus, we are given , so . The probability that a kernel in is also in is .
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