Question

# A doctor knows that the disease meningitis causes the patient to have a stiff neck 50...

A doctor knows that the disease meningitis causes the patient to have a stiff neck 50 % of the time. The doctor also knows that the probability that the patient has meningitis is 1 in 50,000. And the probability that any patient has stiff neck is 1 in 20. Find the probability that a patient with the stiff neck has meningitis. P(stiff_neck|meningitis) = 0.5 P(meningitis) = 1/50,000 P(stiff_neck) = 1/20 P(meningitis|stiff_neck) =?

Given:

P(stiff_neck|meningitis) = 0.5

P(meningitis) = 1/50,000

P(stiff_neck) = 1/20

To find:

P(meningitis|stiff_neck) = P(meningitis and stiff_neck)/P(stiff_neck)

calculations:

P(stiff_neck|meningitis) = P(meningitis and stiff_neck)/P(meningitis)

So, P(meningitis and stiff_neck) = P(stiff_neck|meningitis) * P(meningitis) = 0.5*1/50000 = 1*10-5 = 0.00001

Therefore,

P(meningitis|stiff_neck) = P(meningitis and stiff_neck)/P(stiff_neck) = 0.00001/(1/20) = 20*0.00001 = 0.0002

P(meningitis|stiff_neck) = 0.0002

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