Doctors have devised a test for leptospirosis that has the following

Question

Doctors have devised a test for leptospirosis that has the following property: For any person suffering from lepto, there is a 90% chance of the test returning positive. For a person not suffering from lepto, there is an 80% chance of the test returning negative. It is known that 10% of people who go for testing have lepto. If a person who gets tested gets a +ve result for lepto (as in, the test result says they have got lepto), what is the probability that they actually have lepto?

A. 7/10
B. 8/11
C. 1/3
D. 1/2
E. 5/13

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Official Answer

C

A. 7/10
B. 8/11
C. 1/3
D. 1/2
E. 5/13

Are You Up For the Challenge: 700 Level Questions

Nidzo · Answer

Let the number of people being tested be 100.

We know 10% of those tested have Lepto, so of those being tested 10 will have it and 90 wont.

Positive:  10

There is a 90% chance that someone who is positive will get a positive test result, and 10% that they won't. From 10, 9 will test positive while 1 will test negative.

Negative:  90

There is a 20% chance that someone who is negative will get a positive test result, and 80% that they won't. From 90, 18 will get a positive result while 72 will get a negative test result.

Probability that a positive test is a positive case:   \frac{Number of people who have Lepto}{Total number of positive tests}

Number of people who have lepto is 9. Total positive cases is 9+18 = 27.

= \frac{9}{27}

=1/3

Answer C

pradeepbhuyan · Answer

How number of people who have lepto is 9 
It should be 10

Posted from my mobile device

azulonx · Answer

If we assume total no. People = 100 
Then 10%100= 10

However there’s two scenarios:

Case 1) PEOPLE W LEPO & TESTED POSITIVE:
Independent events:
Probability of selecting lepo: 10/100
Probability of that person testing positive: 90/100 
p(L) * P(t) = 1/10*9/10= 9/100

So out of the 100 people, 9 will have lepo and will test positive

CASE 2) PEOPLE W NO LEPO & FALSE POSITIVE:
P of no lepo: 90/100 
P of testing positive: 20/100
90/100*20/100= 18/100

So 18 people wont have lepo but will test positive.

Question asks for 9/27 =1/3

Dooperman · Answer

Let total ppl = 1000

100 People have lepto. 90 test positive (90%), 10 test negative

900 people dont have lepto. 720 test negative (80%), 180 test positive.

positive cases that tested positive = 90.
Total positive cases = 90 + 180 = 270.

P = 90/270 = 1/3

ZIX · Answer

Have lepto AND result is positive:  (0.1)(0.9)  -- (1) (favourable outcome)
Don't have lepto AND result is positive:  (0.9)(0.2)

Total probability of getting a +ve result:  (0.1)(0.9) + (0.9)(0.2) = 0.27  -- (2) (total outcome)

Divide equation (1) by (2):  \frac{0.09}{0.27} = \frac{1}{3}

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Doctors have devised a test for leptospirosis that has the following

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Doctors have devised a test for leptospirosis that has the following

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