All athletes participating in a high school sports league are required to be tes

Question

All athletes participating in a high school sports league are required to be tested for steroid use. Those who fail are barred from competition for the rest of the year. Research shows that the specific test used for steroids is 95% accurate. Unknown to the coaches, 4% of the athletes actually use steroids. If there are 500 athletes in league, how many of them are likely to fail the test? How many of those are false accusations, resulting in athletes being incorrectly suspended from play? athletes will fail the test, out of the 500 athletes tested. of the athletes who tested positive for steroids actually do not use steroids. They were falsely accused.

Explanation / Answer

Out of 500 athletes, 4% use steroid => 20 use steroids. Since the test is only 95% accurate, it will show positive for only 20 x 0.95 = 19 athletes. So, 19 will fail the test.

Of the remaining 480 athletes, who do not use steroids, only 95% will test negative since the test is only 95% accurate => 456 will pass the test but 24 will fail the test.

Thus, total number of athletes who fail the test would be 19 + 24 = 43 Answer 1

Of the 43 who fail the test, only 19 have actually used steroids and so the number of athletes falsely accused would be 24 Answer 2

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