You go to see the doctor about an ingrown toenail. The doctor selects you at ran

Q: You go to see the doctor about an ingrown toenail. The doctor selects you at ran

a) Probability of receiving a positive test = P(receive positive test | infected)*P(infected) + P(receive positive test | not infected )*P(not infected) = 1*1/10000 + 1%*(1-1/10000) = 1.01 % b) The probability that you have swine flu = 1*1/10000/1.01% = 0.99 % c) In this case, P(infected) = 1/200 = 0.5% Therefore, P(test positive) = 1*0.5%+1%*(1-0.5%) = 1.5 % Revised estimate for the probability that you have the disease = 1*0.5%/1.5% = 33.44%

ID: 388748 • Letter: Y

Question

You go to see the doctor about an ingrown toenail. The doctor selects you at random to have a blood test for swine flu, which for the purposes of this exercise we will say is currently suspected to affect 1 in 10,000 people in America. The test is 99% accurate, in the sense that the probability of a false positive is 1%. The probability of a false negative is zero. You test positive. a) What is the probability of receiving a positive test? (5 points) b) What is the probability that you have swine flu? (5 points) c) Now imagine that you went to a friend’s wedding in Mexico recently, and (for the purposes of this exercise) it is know that 1 in 200 people who visited Mexico recently come back with swine flu. Given the same test result as above, what should your revised estimate be for the probability you have the disease? You go to see the doctor about an ingrown toenail. The doctor selects you at random to have a blood test for swine flu, which for the purposes of this exercise we will say is currently suspected to affect 1 in 10,000 people in America. The test is 99% accurate, in the sense that the probability of a false positive is 1%. The probability of a false negative is zero. You test positive. a) What is the probability of receiving a positive test? (5 points) b) What is the probability that you have swine flu? (5 points) c) Now imagine that you went to a friend’s wedding in Mexico recently, and (for the purposes of this exercise) it is know that 1 in 200 people who visited Mexico recently come back with swine flu. Given the same test result as above, what should your revised estimate be for the probability you have the disease? You go to see the doctor about an ingrown toenail. The doctor selects you at random to have a blood test for swine flu, which for the purposes of this exercise we will say is currently suspected to affect 1 in 10,000 people in America. The test is 99% accurate, in the sense that the probability of a false positive is 1%. The probability of a false negative is zero. You test positive. a) What is the probability of receiving a positive test? (5 points) b) What is the probability that you have swine flu? (5 points) c) Now imagine that you went to a friend’s wedding in Mexico recently, and (for the purposes of this exercise) it is know that 1 in 200 people who visited Mexico recently come back with swine flu. Given the same test result as above, what should your revised estimate be for the probability you have the disease?

Explanation / Answer

Probability of receiving a positive test = P(receive positive test | infected)*P(infected) + P(receive positive test | not infected )*P(not infected)

= 1*1/10000 + 1%*(1-1/10000)

= 1.01 %

b) The probability that you have swine flu = 1*1/10000/1.01% = 0.99 %

c) In this case, P(infected) = 1/200 = 0.5%

Therefore, P(test positive) = 1*0.5%+1%*(1-0.5%) = 1.5 %

Revised estimate for the probability that you have the disease = 1*0.5%/1.5% = 33.44%

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