Suppose that 2% of a population are infected with a potentially fatal and contagious virus. A test for the virus is developed. The test identifies correctly (results in positive result) 99% of those carrying the virus. Of those not infected, the test gives a positive result in 0.5% of cases.

1. If we randomly select a test, what is the probability that the test is positive? Round to the 4 decimal places.

2. Given a positive test, what is the possibility that a person is actually infected? Round to 3 decimal places.

3. In a British crime survey the following statistics were found. The whole population contains half of women and half of men. Of all women, 21% were worried about crime, and of all men, 8% were worried. Given a person who is worried about crime, what is the probability he is male? Round to 3 decimal places.