Wizard
Joined: Oct 14, 2009
• Posts: 22831
December 25th, 2011 at 9:40:59 AM permalink

Either I misunderstand the question or Marilyn does. I interpret the question to be what is the likelihood any one employee is chosen at least once over the course of a year.

My answer to that would be 1-(1-.25)^4 = 68.36%. In other words the probability of escaping four drug tests is .75*.75*.75*.75. So the chances of getting picked at least once is 1-.75*.75*.75*.75.

As an aside, if the probability of being chosen is p, and the number of tests is 1/p, as p approaches zero the probability of being selected at least once approaches (e-1)/e.

This is by far the first time I have taken issue with Marilyn's responses. She really stirred up the pot with a bad answer to the Monty Hall question.

How do you interpret the question being asked?
It's not whether you win or lose; it's whether or not you had a good bet.
duckmankilla
Joined: Nov 25, 2011
• Posts: 236
December 25th, 2011 at 9:46:55 AM permalink
I would say that your interpretation makes the most sense in response to the reader's question... although I think you may have also had a typo yourself when you stated "This is by far the first time I have taken issue with Marilyn's responses. She really stirred up the pot with a bad answer to the Monty Hall question", as these seem to be separate issues unless i am mistaken. If she were interpreting the question as "what are the chances that an individual is chosen in EACH INDIVIDUAL random drug test", then 25% would seem to be accurate, but as I believe the question was intended, I'd agree with your figures.

Merry Christmas to all.
pacomartin
Joined: Jan 14, 2010
• Posts: 7895
December 25th, 2011 at 10:01:39 AM permalink
Quote: Wizard

How do you interpret the question being asked?

I think one of her associates filled in and wrote the Christmas column. It seems like a really stupid answer, and is not characteristic of her. I don't see any other way of interpreting the question except your way. I'll bet she gets a ton of mail.

It is already being referred to as the infamous Ask Marilyn Christmas column on this forum.
AZDuffman
Joined: Nov 2, 2009
• Posts: 12332
December 25th, 2011 at 10:22:06 AM permalink
I am going to vote with Wiz on this one. Even without doing the math you can see that you have a greater than 25% chance at being selected. Her answer would be similar to saying "what are the chances of guessing a coin-flip right over 2 flips?" and an answer of "50%." This is first level statistics stuff.
All animals are equal, but some are more equal than others
SOOPOO
Joined: Aug 8, 2010
• Posts: 7794
December 25th, 2011 at 10:53:38 AM permalink
Wow- I would consider her answer a fireable offense. To make an error on such a simple question when you tout yourself as an expert....
CrystalMath
Joined: May 10, 2011
• Posts: 1889
December 25th, 2011 at 10:59:11 AM permalink
Of course, she's wrong. I wonder if she is humble enough to admit it.

As I recall, Statman had a special fondness of Marylin, and I'm pretty sure that he would even agree that she is wrong.
I heart Crystal Math.
Doc
Joined: Feb 27, 2010
• Posts: 7070
December 25th, 2011 at 11:20:27 AM permalink
I, too, agree with the Wizard.

I also have disagreed with Marilyn multiple times, and I even pick on things other than her logic and explanations. Back in November 2007, she wrote about a problem in which the key was related to the Hawaiian alphabet. She referred to Hawaii as "our westernmost state." I took issue with that, but, of course, I never got a reply to my email.
Wizard
Joined: Oct 14, 2009
• Posts: 22831
December 25th, 2011 at 11:36:37 AM permalink
Quote: Doc

She referred to Hawaii as "our westernmost state." I took issue with that, but, of course, I never got a reply to my email.

Nice catch! I once wrote to Marilyn about something by postal mail, enclosing a SASE, and didn't get a reply either.

It's not whether you win or lose; it's whether or not you had a good bet.
Doc
Joined: Feb 27, 2010
• Posts: 7070
December 25th, 2011 at 12:09:53 PM permalink
Quote: Wizard

Nice catch!

I suggested she refer to Hawaii as our "southernmost" state. I am such a nerd on these things that I view Alaska as not only our westernmost and northernmost state, but also our easternmost state.
pacomartin
Joined: Jan 14, 2010