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Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were allergic to penicillin, Nathan had a 75% chance of having the same allergy. The doctor performed a skin test to see whether Nathan would react to it. The test is 98% accurate. What is the probability that Nathan is allergic to penicillin and the test predicts it? A. 0.005

B. 0.015

C. 0.245

D. 0.735

Respuesta :

Nathan has an infection and he needs to be treated with penicillin
But there’s a 75% probability of him being allergic to penicillin
And to test if the skin reacts to penicillin, the test is 98% accuracy
So even if he has the allergy the test is only 98% accurate of identifying the allergy
Therefore we are asked to find the probability of both these events happening
Event 1 and event 2 both should happen then. When the ‘and’ function is used in probabilities then the probabilities of both events happening should be multiplied
Therefore probability that Nathan has the allergy and test predicts it is
= 75% x 98% = 0.735
The answer is D. 0.735

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