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In: Statistics and Probability

If an infected person is tested for corona, the probability that the test will give a...

If an infected person is tested for corona, the probability that the test will give a positive result is 0.60 and if this person is not infected the probability that it will give a positive result is 0.10. Suppose that 2% of the people are corona infected. If one random person is tested for corona using this test, then the probability that the test will give a positive result is

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Expert Solution

If an infected person is tested for corona, the probability that the test will give positive result, is 0.60.

So,

If a person is not infected , the probability that it will give a positive result is 0.10.

2% of the people are corona infected.

So, the probability that a randomly selected person is corona infected, is 0.02.

So, the probability that a randomly selected person is not corona infected, is 1-0.02, ie. 0.98.

So,

We have to find the probability that the test will give a positive result, for a random person.

Now,

Now, by total probability theorem, this becomes

So, the probability that a random individual tests positive, is 0.11.

orchestra answered 1 year ago
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