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
Thanks to the invention of a new device, the
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?
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)
P(Cancer affected) = P(affected) = 2% = 0.02
So, P(not affected) = (1-0.02) = 0.98
Using formula,
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