Question

8. A certain virus infects one in every 700 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. (a) Find the probability that a person has the virus given that they have tested positive. (b) Find the probability that a person does not have the virus given that they have tested negative.

Answer 1

Part a

Find the probability that a person has the virus given that they have tested positive

Probability in fraction form

p=(1/700)*(90/100)=90/70,000

simplify

P=9/7,000

Part b

Find the probability that a person does not have the virus given that they have tested negative

Probability in fraction form

P=(699/700)*(10/100)

P=6,990/70,000

simplify

P=699/7,000