Question

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

Answer 1

The answer is D. 0.735

Step-by-step explanation:

chance of having the same allergy. = 75%

accuracy of test = 98%

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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