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4 days ago

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Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were all

ergic 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?

2 answers:

PIT_PIT [3.9K]4 days ago

7 0

Answer:

0.735

Step-by-step explanation:

Let A denote the event of being allergic to penicillin and T represent the event where the test conclusively predicts the allergy.

<pBased on the question,

There's a 75% likelihood of having the allergy.

⇒ Probability of being allergic to penicillin, P(A) = 75 % = 0.75,

The test also shows a 98% accuracy.

⇒ The probability that the test indicates the allergy, P(B) = 98% = 0.98

Given that A and T are independent events,

Hence, the probability of Nathan being allergic to penicillin and the prediction being accurate

= P(A) × P(T)

= 0.75 × 0.98

= 0.735

AnnZ [3.9K]4 days ago

3 0

Nathan has a 73.5% probability of being allergic to penicillin, as indicated by the test.

Calculating: 75% * 98% = 73.5%

.75 *.98 =.735

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