A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Question
100%

Thanks to the invention of a new device, the probability of
detecting cancer in an affected person is 99%.
However, this machine could diagnose cancer
in a person who does not have cancer in one case in 10,000.
If 2% of the population of a region has cancer,
what is the probability that someone in this population will be diagnosed with cancer? Knowing that a person
is diagnosed with cancer, what is the probability that it will
really is it?

Expert Solution
Check Mark
Step 1: Introduce the given information

According to the given information,

The probability of detecting cancer in an affected person is, P(diagnosed | affected) = 99% = 0.99

The probability of diagnose cancerin a person who does not have cancer is, P(diagnosed | not affected)equals 1 over 10000 equals 0.0001

P(Cancer affected) = P(affected) = 2% = 0.02

So, P(not affected) = (1-0.02) = 0.98

Using formula,

P left parenthesis A vertical line B right parenthesis equals fraction numerator P left parenthesis B vertical line A right parenthesis cross times P left parenthesis A right parenthesis over denominator P left parenthesis B vertical line A right parenthesis cross times P left parenthesis A right parenthesis plus P left parenthesis B vertical line A to the power of c right parenthesis cross times P left parenthesis A to the power of c right parenthesis end fraction

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