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 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. If the test predicts that Nathan is not allergic to penicillin, what is the probability after the test that Nathan is not allergic to the drug?

Answer 1

Answer Choices are:
0.1135

0.2450

0.9423

0.9932

Answer 2

@Squirrels

Answer 3

Ok well... the test is 98% accurate.
What is 98% in decimal form?

Answer 4

.98

Answer 5

Good! Now do you know what to do? It's pretty simple.

Answer 6

No what should I do now?

Answer 7

Ok thats fine. Out of 100% accuracy, there is 98%, correct? Well 98% is .98 in decimal form, and 1.00 is 100%. What is the inaccuracy in decimal form?

Answer 8

What do you mean inaccuracy?

Answer 9

Well the test is 98% sure that he is allergic to penicillin. That means the test in 2% inaccurate. (.2) Do you get what i mean?

Answer 10

yes

Answer 11

Oops sorry i mean to say 0.02*

Answer 12

0.2450 So would that be the answer?

Answer 13

@Squirrels

Answer 14

@lacrosseplayer22

Answer 15

Please help

Answer 16

@iPwnBunnies

Answer 17

Do you know Bayes Theorem?

Answer 18

No @ybarrap

Answer 19

Let Event A be the event that Nathan is allergic to penicillin
Let Event B be the event that the penicillin test comes out positive given that Nathan has the allergy

We want the probability that Nathan is not allergic to penicillin and the test comes out positive: P(A)*P(B)=(1-.75)*0.98.

Does this make sense?

Answer 20

Yes it does @ybarrap

Answer 21

good luck :)

Answer 22

@M.D.Saxon

Answer 23

sorry idk sorry

Answer 24

Correction:

We want the probability that Nathan is not allergic to penicillin and the test comes out positive: $$\large {\left (1-P(A)\right )\times P(B)=(1-.75)*0.98}$$