A disease strikes 1 in 25 students. A new test correctly diagnoses if one has it...

A disease strikes 1 in 25 students. A new test correctly diagnoses if one has it 95% of the time and correctly confirms that one does not have it 97% of the time. If you tested positively for the it, what is the probability that you actually have it?

Expert Solution

P(have the disease) = 1/25 = 0.04

P(test positive) = P(test positive | have the disease) * P(have the disease) + P(test positive | does not have the disease) * P(does not have the disease)

= 0.95 * 0.04 + 0.97 * (1 - 0.04)

= 0.9692

P(have the disease | test positive) = P(test positive | have the disease) * P(have the disease)/P(test positive)

= (0.95 * 0.04)/0.9692

= 0.0392

orchestra answered 1 year ago

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