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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 has 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 not allergic to penicillin and the test predicts it?

Respuesta :

luisejr77

Answer:

The probability is 0.245

Step-by-step explanation:

Call B the event: Nathan is allergic to penicillin.

We know from your family history that

[tex]P(B) = 0.75[/tex]

So the probability that Nathan is not allergic to penicillin is

[tex]P(\~B) = 1-P(B) = 0.25[/tex]

Then, the test has 98% accuracy, that is: The probability that the test result is correct is 0.98.

So the probability that the test predicts that Nathan is not allergic and is not really allergic is:

[tex]P = 0.25 * 0.98 = 0.245[/tex]

There is a 24.5% chance that Nathan is not allergic and the test predicts it

Answer:

C = .9423

Step-by-step explanation:

i took the test and got it right .