Marilyn apologizes for mistake in drug-testing answer

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Marilyn apologizes for mistake in drug-testing answer

Postby Anna Melissa » Sat Jan 21, 2012 9:49 am

From "Ask Marilyn" in Parade, dated January 22, 2012:

When a reader wrote about randomly selecting 100 out of 400 employees each quarter for drug testing, he asked about the chances of an individual being chosen over the course of a year. You answered a different question: "If an individual has not been selected over the first three quarters, what are the chances that he or she will be chosen in the fourth quarter?" The answer to the latter question is indeed 25 percent, as you wrote, but the answer to the former is about 68 percent. --George Land, Tyler, Tex.

You're right, and I apologize for the mistake. My neurons must have been napping.

The reasoning works like this: Of the 400 names, 25 percent (100) are selected in the first quarter. Assume "perfect" randomization for the purpose of calculation: Of the 300 that weren't chosen, 25 percent (75) would be selected in the second quarter. Of the 225 still-unchosen names, 25 percent (about 56) would be selected in the third. And of the 169 remaining unchosen names, 25 percent (about 42) would be selected in the fourth.

So a total of 273 different people (100 + 75 + 56 + 42 = 273) will have been selected--about 68 percent of all the employees. (Many names will have been chosen more than once, so 400 tests are still administered.) Yet the chance of any individual's name being chosen in the next random selection (or any future selection) never rises above 25 percent.
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Postby robert 46 » Mon Jan 23, 2012 10:07 am

Marilyn's definitive answer. Obviously, she merely misinterpreted the question in her first response.
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