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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 $\frac{1}{50000}$, and that the proportion od people having stiff neck is $\frac{1}{20}$. Then the percentage of people who had meningtis and complain about stiff neck is:

1. 0.01%
2. 0.02%
3. 0.04%
4. 0.05%

We can solve this using Bayes formula:

P(B|A) = P(A|B)·P(B) / P(A)

Assume A refer to stiff neck and B refer to probability of meningitis,

P(A|B) = meningitis causes stiff neck =50%= 0.5

P(A)=1/20

P(B)= 1/50000

P(B|A) = 0.5*1/50000/(1/20)= 0.02%

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