Question

You go to see the doctor. 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. The test is 96% accurate, in the sense that the probability of a false positive is 4%. The probability of a false negative is zero. You test positive. What is the new probability that you have swine flu? (round to the nearest thousands place … 3 decimal places)

True or False: Hill climbing could be considered a greedy technique in that it will opt to retain a change to a neighbor value if the new state has a better outcome than the previous state.

Select one:

True

False

Answer 1

Q:- You go to see the doctor. 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. The test is 96% accurate, in the sense that the probability of a false positive is 4%. The probability of a false negative is zero. You test positive.
What is the new probability that you have swine flu? (round to the nearest thousands place … 3 decimal places)

Answer:--------
Let P(D) be the probability you have swine flu.
Let P(T) be the probability of a positive test.
We wish to know P(D|T).

Bayes theorem says,
P(D|T) = P(T|D)P(D) / P(T)

which in this case can be rewritten as
P(D|T) = P(T|D)P(D) / (P(T|D)P(D) + P(T|ND)P(ND))

where, P(ND) means the probability of not having swine flu.

We have,
P(D) = 0.0001 (the a priori probability you have swine flu).
P(ND) = 0.9999

P(T|D) = 1 (if you have swine flu the test is always positive).
P(T|ND) = 0.04 (4% chance of a false positive).

Plugging these numbers in we get
P(D|T) = 1*0.0001 / (1*0.0001 + 0.04*0.9999)
= 1*0.0001 / (0.0001+0.039996 )
= 0.0001 / 0.040096
≈ 0.002

That is, even though the test was positive your chance of having swine flu is only .2%. (This is essentially the “defense attorney’s” argument we discussed in the lectures, though in this case it’s not a fallacy because your P(D) is indeed very low.)

Q:- Hill climbing could be considered a greedy technique in that it will opt to retain a change to a neighbor value if the new state has a better outcome than the previous state.
Answer:-----
True