Marilyn Vos Savant - Errors in The Column

Errors in The Column

On 22 January 2012 vos Savant admitted a mistake in her column. In the original column, published on 25 December 2011, a reader asked:

I manage a drug-testing program for an organization with 400 employees. Every three months, a random-number generator selects 100 names for testing. Afterward, these names go back into the selection pool. Obviously, the probability of an employee being chosen in one quarter is 25 percent. But what is the likelihood of being chosen over the course of a year? —Jerry Haskins, Vicksburg, Miss.

Marilyn's response was:

The probability remains 25 percent, despite the repeated testing. One might think that as the number of tests grows, the likelihood of being chosen increases, but as long as the size of the pool remains the same, so does the probability. Goes against your intuition, doesn't it?

The correct answer is around 68%, calculated as the complement of the probability of not being chosen in any of the four quarters: 1-0.754.