A food manufacturer is analyzing a sample of 500 corn kernels for the presence of a toxin. In this sample, three kernels have dangerously high levels of the toxin. If 10 kernels are randomly selected from the sample, what is the probability that exactly one kernel contains a dangerously high level of the toxin?

Answered: A food manufacturer is analyzing a…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.8: Probabilities Of Disjoint And Overlapping Events

Problem 2C

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A food manufacturer is analyzing a sample of 500 corn kernels for the presence of a toxin. In this sample, three kernels have dangerously high levels of the toxin. If 10 kernels are randomly selected from the sample, what is the probability that exactly one kernel contains a dangerously high level of the toxin?

Expert Solution

Step 1 Outcomes

In the given case, the total sample size (n) is 500.

Assuming X to represent the number of kernels out of 10 randomly selected Kernels that have the toxin. the PDF of X is given by:

$\begin{array}{rcl} P (X) & = & \frac{{}^{3}C_{x} \times {}^{497}C_{10 - x}}{{}^{500}C_{10}} \end{array}$

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