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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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Suppose the probability of a false positive result on a mammograrn is 4 % and that radiologists’ interpretations of mammograms are mutually independent in the sense that whether or not a radiologist finds a positive result on one mammogram does not influence whether or not a radiologist finds a positive result on another mammogram. Assume that a woman has a mammogram every year for ten years.
a. What is the probability that she will have no false positive results during that time?
b. What is the probability that she will have at least one false positive result during that time?
c. What is the probability that she will have exactly two false positive results during that time?
d. Suppose that the probability of a false negative result on a mammogram is 2 % , and assume that the probability that a randomly chosen woman has breast cancer is 0.0002.
(i) If a woman has a positive test result one year, what is the probability that she actually has breast cancer?
(ii) If a woman has a negative test result one year, what is the probability that she actually has breast cancer?

To determine

(a)

To find out the probability that woman will have no false positive results during that time.

Explanation

Given information:

The probability of false positive result on a mammogram is 4%. Assume that a woman has a mammogram every year for ten years.

Calculation:

According to the given information the following things can be written

let us say p=probability of false positive result=0

To determine

(b)

To find out the probability that woman will have at least one false positive results during that time.

To determine

(c)

To find out the probability that woman will have exactly two false positive results during that time.

To determine

(d)

To find out the probability that 1) woman actually has breast cancer if she has a positive test result one year. 2)Woman actually has breast cancer if she has a negative test result one year.

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