The test to determine the presence of a certain virus in a pigeon is 97% accurate for a pigeon that has the virus and 99% accurate for a pigeon that does not have the virus. In a given population, 1.5% of the pigeons are infected.
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The probability that a randomly selected pigeon gets an incorrect result is

1.5% pigeons are infected and inaccuracy of the test is 1-97% = 3% and the rest of 1-1.5% = 98.5% pigeons people are un-infected and inaccuracy of test for that is 1-99% = 1% .

0.03 and 0.01 are the probability of an error being made in infected and un-infected respectively while probability of infected and un-infected are 0.015 and 0.985 respectively.

So the probability of a randomly chosen person gets an incorrect result is

= 0.03*0.015 + 0.985*0.01

= 0.0103

joaobezerra joaobezerra · Answer 2 · 2021-08-06T15:46:13+02:00

Before finding the probabilities, we need to find all possible outcomes, and it's probabilities.

Doing this, we get:

The probability that a randomly selected pigeon gets an incorrect result is 0.0103 = 1.03%.

Possible outcomes:

Pigeon has the virus(1.5% probability) and gets an accurate test, showing the presence of the virus(97% probability).

Pigeon has the virus(1.5% probability) and gets an inaccurate test, not showing the presence of the virus(100% - 97% = 3% probability).

Pigeon does not have the virus(100 - 1.5 = 98.5% probability) and gets an accurate test, not showing the presence of the virus(99% probability).

Pigeon does not have the virus(98.5% probability) and gets an innacurate test, showing the virus(100 - 99 = 1% probability).

Probability of incorrect result:

Has the virus and test negative: 0.03 of 0.015

Does not have the virus and test positive: 0.01 of 0.985

Thus:

[tex]p = 0.03\times0.015 + 0.01\times0.985 = 0.0103[/tex]

The probability that a randomly selected pigeon gets an incorrect result is 0.0103 = 1.03%.

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