Question

3. The flu virus infects 1 in every 250 people. The test used to detect the flu shows a positive result 70% of the time when the person actually has the flu and shows a positive result 15% of the time when a person does not have the flu. Event A will be a “person who is infected”. Event B will be a “person who tests positive.” Hint: Use a tree diagram.

(a) Given that a person tests positive, what is the probability that the person is infected?

13(a) _________

(b) Given that a person is not infected, what is the probability that the person tests

negative?

13(b) _______

Answer 1

I have answered the question below

Please up vote for the same and thanks!!!

Do reach out in the comments for any queries

Answer:

a)

Bayes' Theorem: P(A | B) = P(A & B) / P(B)

P(has virus | tested positive) = P(has virus and tested positive) / P(tested positive)

= P(has virus and tested positive) / [P(has virus and tested positive) + P(doesn't have virus and tested positive)]

= (0.004 x 0.7) / [(0.004 x 0.7) + (0.996 x 0.15)]

=0.0184

b)

P(tests negative | does not have virus) = P(tests negative and does not have virus) / P(does not have virus)

= P(tests negative and does not have virus) / [P(does not have virus and tested negative) + P(doesn't have virus and tested positive)]

= (0.996*0.85)/((0.996*0.85)+(0.996*0.15))

= 0.85