The answer is 0.2450
To calculate this, a multiplication rule is used. The multiplication rule calculates the probability that both of two events will occur. In this method, the probabilities of each event are multiplied.
In this situation, we have two events occurring simultaneously:
1. Nathan is not allergic to penicillin. The probability that Nathan is not allergic to penicillin is:
1 - the probability of having the allergy.
If the probability of having the allergy is 75% = 0.75, then the probability that Nathan is not allergic to penicillin is:
1 - 0.75 = 0.25
2. The probability that the test is accurate: 98% = 0.98.
By using the multiplication rule:
0.25 × 0.98 = 0.245
Therefore, the probability after the test that Nathan is not allergic to the drug is 0.245 = 24.5%.
