December2015 Cs Q32

0. Suppose that from given statistics, it is known that meningitis causes stiff neck 50% of the time, that the proportion of persons having meningitis is 1/50000, and that the proportion of people having stiff neck is 1/20. Then the percentage of people who had meningitis and complain about stiff neck is:

Answer
Comment
Array

Option : B
Explanation :
The computation is based on the simplified Bayes’ formula.
P{B|A} = (P{A|B}·P{B) / P{A}.
P{M|S} = probability that a person had meningitis, conditioned by the existence of stiff neck.
P{S|M} = probability that a person complains about stiff neck, conditioned by the existence of meningitis. = 50%=1/2
P{S} = proportion of people who complain about stiff neck. = 1/20
P{M} = proportion of people who had meningitis. = 1/50,000
Then:
P{M|S} = (P{S|M}·P{M}) / P{S} =( 1 / 2 x 1 / 50,000 ) / 1 / 20 = 0.0002 = 0.02%

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