Answer:
0.5 = 50%
Step-by-step explanation:
There is a false positive when 2 events occur:
1. The man being tested does not have prostate cancer.
2. The test says the man has prostate cancer, which occurs when the man has high PSA levels
If a man has prostate cancer, a positive test is a true positive and a negative test is a false negative. If a man does not have prostate cancer and tests negative, that is a true negative.
The probability that a man being tested does not have prostate cancer = 1 - probability that a man being tested has prostate cancer = 1 - 25% = 0.75
The probability that a man being tested does not have prostate cancer AND has a high PSA level = 2/3 of people without prostate cancer = 2/3 of 0.75 = 0.5.
This is because 2/3 men without prostate cancer have high PSA levels, so 2/3 of all men that don't have prostate cancer will test positive. This accounts for all men that do not have prostate cancer and have high PSA levels
