Some states have recently initiated programs to randomly test high school athlet

Question

Some states have recently initiated programs to randomly test high school athletes for possible use of anabolic steroids after concerns arose about the health of the athletes and fairness in the sports. Critics of the programs say that the amount of money spent on testing isn’t worth it, since only 1 in 2000 high school athletes actually use steroids to enhance their performance. The test used does have a 97.3% chance of being positive when an athlete uses steroids and a 98.4% chance of showing a negative result when an athlete is not using steroids. (a) (6 points) What is the chance that the test is negative when an athlete is using steroids?

Explanation / Answer

Let A shows the event that athlete uses steroids and B shows the event that athlete did not use steroids. So we have

P(A) = 1 / 2000 = 0.0005

P(B) = 1 - 0.0005 = 0.9995

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Let P shows the event that test gives positive results and N shows the event that test gives negative results. So

P(P | A) = 0.973

P(N | A) = 1 - 0.973 = 0.027

and

P(N | B) = 0.984

P(P | B) = 1 - 0.984 = 0.016

(A)

The chance that the test is negative when an athlete is using steroids, P(N | A) is

P(N | A) = 1 - 0.973 = 0.027

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