Question

In: Statistics and Probability

Suppose 3% of all athletes are actually using the endurance-boosting hormone EPO. The test for the...

Suppose 3% of all athletes are actually using the endurance-boosting hormone EPO. The test for the presence of this substance is very reliable; the probability of a positive test result given the presence of EPO is 0.99, and the probability of a negative test result when EPO is not present is 0.90. Find the probability that a randomly selected athlete tests positive for the presence of EPO.

Group of answer choices

0.9027

0.1267

0.0297

0.0567

Expert Solution

Answer:-

Given That:-

Suppose 3% of all athletes are actually using the endurance-boosting hormone EPO. The test for the presence of this substance is very reliable; the probability of a positive test result given the presence of EPO is 0.99, and the probability of a negative test result when EPO is not present is 0.90. Find the probability that a randomly selected athlete tests positive for the presence of EPO.

Group of answer choices

0.9027

0.1267

0.0297

0.0567

Given,

3% of all athletes are actually using the endurance-boosting hormone EPO.

Prob [Test result comes poistive given the presence of EPO] = 0.99

and

prob [Test result comes negative given the absence of EPO] = 0.90

Therefore,

The probability that a randomly selected athletes tests positive for the presence of EPO = 3/100 * 99/100

= 297/10000

= 0.0297

The probability that a randomly selected athletes tests positive for the presence of EPO = 0.0297

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orchestra answered 1 year ago

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