# Ask Marilyn: What's the Probability of Being Chosen for a Drug Test?

#### Alexmahone

##### Active member

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’s the likelihood of being chosen over the course of a year?

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?
— Marilyn vos Savant
Would someone please explain this to me? It goes against my intuition as well.

---------- Post added at 11:19 PM ---------- Previous post was at 11:05 PM ----------

I think the answer should be 1-P(chosen no times)$=1-0.75^4\approx 0.68$

#### CaptainBlack

##### Well-known member

Would someone please explain this to me? It goes against my intuition as well.

---------- Post added at 11:19 PM ---------- Previous post was at 11:05 PM ----------

I think the answer should be 1-P(chosen no times)$=1-0.75^4\approx 0.68$
Well I think your answer is correct. It is not unknown for vos Savant to be wrong, but it may be that she is answering a different interpretation of the question (if true it is a very odd interpretation).

I quote form Wikipedia:

Errors in the ColumnOn January 22, 2012 Vos Savant admitted a mistake in her column for perhaps the first time ever. The original column was published on December 25, 2011, when 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 complementary of the probability of not being chosen in any of the four quarters: 1 - 0.75^4.[15]
CB

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#### Plato

##### Well-known member
MHB Math Helper
Well I think your answer is correct. It is not unknown for vos Savant to be wrong, but it may be that she is answering a different interpretation of the question (if true it is a very odd interpretation).

#### ThePerfectHacker

##### Well-known member
I know this is off topic but I just wanted to say that I think that Marilyn vos Savant is one of those people where the masses think is some brilliant thinker. I do not. I see nothing brilliant about her. She has this recognition because she apparently has the highest recorded IQ score.

I want to put it into perspective. According to IQ researchers they estimate the Gottfried von Leibniz had his estimated at 210 and Johann Wolfgang von Goethe estimated at 205. No one can possibly say that she is more brilliant than either of these two people as she has a higher IQ score. It is just that the masses think that incredibly high IQ is a measure of brillinace and hence they look at her as an intellectual godess.

Here is an example that will hopefully convince you that she is not very smart. She wrote a book in 1993/1994 when Andrew Wiles proved Fermat's Last Theorem explaining why he is wrong. Apparently her "explanation" was layman popular mathematics that had nothing to do with anything of his work. The approach that Wiles took was something way beyond her, so she made up non-sense about why he is wrong. Does a brilliant person made such idiotic mistakes?

#### CaptainBlack

##### Well-known member
I know this is off topic but I just wanted to say that I think that Marilyn vos Savant is one of those people where the masses think is some brilliant thinker. I do not. I see nothing brilliant about her. She has this recognition because she apparently has the highest recorded IQ score.

I want to put it into perspective. According to IQ researchers they estimate the Gottfried von Leibniz had his estimated at 210 and Johann Wolfgang von Goethe estimated at 205. No one can possibly say that she is more brilliant than either of these two people as she has a higher IQ score. It is just that the masses think that incredibly high IQ is a measure of brillinace and hence they look at her as an intellectual godess.

Here is an example that will hopefully convince you that she is not very smart. She wrote a book in 1993/1994 when Andrew Wiles proved Fermat's Last Theorem explaining why he is wrong. Apparently her "explanation" was layman popular mathematics that had nothing to do with anything of his work. The approach that Wiles took was something way beyond her, so she made up non-sense about why he is wrong. Does a brilliant person made such idiotic mistakes?
The highest numbers reported for Ms Vos Savant have been shown to misreported results and/or misuse of an obsolete test. Even the more modest 186 is for a test that has been criticised for improper design and scoring.

I think all we can say is that she scores highly on such tests. The relevance of such scores to achievement and/or what others might categorise as intelligence is debatable.

The most laughable IQ nonsense that I have come across the the estimation of IQ scores for people who never took such a test, forget Leibniz and Goethe, what about Andy Worhol with an IQ of 86!

CB

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