Question

suppose that 4% of the patients tested in a clinic are infected with avian influenza. furthermore, suppose that when a blood test for avian influenza is given, 97% of the patients infected with avian influenza test positive and that 2% of the patients not infected with avian influenza test positive. what is the probability that a) a patient testing positive for avian influenza with this test is infected with it? b) a patient testing positive for avian influenza with this test is not infected with it? c) a patient testing negative for avian influenza with this test is infected with it? d) a patient testing negative for avian influenza with this test is not infected with it?

Answer 1

To determine the probability that a patient testing positive for avian influenza is infected with it, we can use conditional probability. By calculating the probability using the given information and applying the formula for conditional probability, we find that the probability is approximately 0.67.

Step-by-step explanation:

To determine the probabilities in this scenario, we can use conditional probability. Let's define the events as follows:

A: Patient is infected with avian influenza

B: Patient tests positive for avian influenza

To answer the given questions:

a) P(A|B): Probability that a patient testing positive for avian influenza is infected with it

= P(A ∩ B) / P(B)

= 0.04 * 0.97 / (0.04 * 0.97 + 0.96 * 0.02)

= 0.0388 / (0.0388 + 0.0192)

= 0.0388 / 0.058 = 0.67 (rounded to 2 decimal places)

Therefore, the probability that a patient testing positive for avian influenza is infected with it is approximately 0.67.