Answer to Question #254534 in Statistics and Probability for talie

Question

Suppose that in a certain country the probability that a male is covid-19 positive is 0.2 and that a female is covid-19 positive is 0.15. Also suppose that 50% of the population is female and that a test shows negative for 1% of people who are covid-19 positive and shows positive 0.2% of people who are covid-19 negative. (a) for a female, what is the probability that she is actually covid-19 positive if a test shows positive. (b) if a sample tests positive, what is the probability that it came from a man? 

Answer 1

(a)

From the given data, the following Table is calculated:

P(Female is actually covid-19 positive.GIVEN.Test positive) = P(Female is actually covid-19 positive.AND.Test positive) / P(Test positive)

= 0.1485/ 0.1502

= 0.9887

Answer:

0.9887

(b)

From the given data, the following Table is calculated:

P(Male.GIVEN.Test positive) = P(Male.AND.Test positive) / P(Test positive)

= 0.10/0.175

= 0.5714

Answer:

0.5714