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Introduction to Probability | 1st Edition | ISBN: 9781466575578 | Authors: Joseph K. Blitzstein, Jessica Hwang
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A group of 21 women and 14 men are enrolled in a medical study. Each of them has a

Chapter 9, Problem 3

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QUESTION:

A group of 21 women and 14 men are enrolled in a medical study. Each of them has a certain disease with probability p, independently. It is then found (through extremely reliable testing) that exactly 5 of the people have the disease. Given this information, what is the expected number of women who have the disease? Again given this information, what is the expected number of women who have the disease?

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QUESTION:

A group of 21 women and 14 men are enrolled in a medical study. Each of them has a certain disease with probability p, independently. It is then found (through extremely reliable testing) that exactly 5 of the people have the disease. Given this information, what is the expected number of women who have the disease? Again given this information, what is the expected number of women who have the disease?

ANSWER:

Step 1 of 2

A group of 21 women and 14 men are enrolled in a medical study. Each of them has a certain disease with probability p, independently. It is then found (through extremely reliable testing) that exactly 5 of the people have the disease.

Based on the given information, to find the expected number of women who have the disease.

Let be the random variable that denotes the number of people having the disease, the number of men having the disease is represented by and the number of women having the disease is represented by .

To find .

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