rzervakos19
Joined: Aug 15, 2011
• Posts: 2
August 15th, 2011 at 10:41:01 PM permalink
A statistics question that is too difficult to work through on my own.

Scenario: I (uncomfortably enough) run into the same person in the work bathroom *far* too frequently. There are often days when I will cross paths with this person three times in the bathroom. My wife, who works with me, says that we both must just have tiny bladders but she is afraid of math and I am not. So here is my question: assuming we both go to the bathroom five times a day, for four minutes a trip, and we work shifts that overlap for an eight hour period, and we take a one hour lunch at random times, what is the probability that we would cross paths three times in one day? And beyond that, how likely is that to happen twice a week, for example? Is this simply within the realm of probability or is it unlikely enough to suspect that some sort of nefarious intent is involved?

Long time reader of the wizard of odds site and staunch defender of all tips and strategies within to any unenlightened gamblers within earshot. I hope to put this mystery to rest and I rely on you.

Thanks!
odiousgambit
Joined: Nov 9, 2009
• Posts: 8606
August 16th, 2011 at 1:56:13 AM permalink
can't do the math but will say it sounds creepy if this person wants to go when you go. Twice a week sounds like no big deal though.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
s2dbaker
Joined: Jun 10, 2010
• Posts: 3259
August 16th, 2011 at 2:53:16 AM permalink
I have a similar issue where I work. I concluded that the other guy simply hides in the bathroom when he's stressed out from work since he's usually already there staring at himself in the mirror.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
matilda
Joined: Feb 4, 2010
• Posts: 317
August 16th, 2011 at 8:46:51 AM permalink
Quote: rzervakos19

A statistics question that is too difficult to work through on my own.

Scenario: I (uncomfortably enough) run into the same person in the work bathroom *far* too frequently. There are often days when I will cross paths with this person three times in the bathroom. My wife, who works with me, says that we both must just have tiny bladders but she is afraid of math and I am not. So here is my question: assuming we both go to the bathroom five times a day, for four minutes a trip, and we work shifts that overlap for an eight hour period, and we take a one hour lunch at random times, what is the probability that we would cross paths three times in one day? And beyond that, how likely is that to happen twice a week, for example? Is this simply within the realm of probability or is it unlikely enough to suspect that some sort of nefarious intent is involved?

Long time reader of the wizard of odds site and staunch defender of all tips and strategies within to any unenlightened gamblers within earshot. I hope to put this mystery to rest and I rely on you.

Thanks!

Rate: 5/8 hr day = 5/480 minutes= .01041664/ min or

E(x) = 4 x .0104166 = .0416664/ 4 min per trip.

Three meetings : P(X) = 3 = poisson distribution with mean = .0416664 evaluated at X = 3

P(3) =[( e^-.0416664 ) (.0416664^3) ] / 3! = .000001

Happen twice a week. (Binomial p=.000001, n=5, no. of successes x = 2 )= 9.999932 exp -12 = .000000000009999321
ChampagneFireball
Joined: May 2, 2010
• Posts: 118
August 16th, 2011 at 9:03:19 AM permalink
But people don't go to the bathroom at random times. You don't have the same chance of going to the bathroom 5 minutes after the last trip as you do 90 minutes after.
CrystalMath
Joined: May 10, 2011
• Posts: 1894
August 16th, 2011 at 9:13:20 AM permalink
This is quite humorous.

Matilda's statistics assume that you go to the bathroom at random times during the day, but this can't be entirely true. For instance, you are likely to go to the bathroom an hour after your morning coffee. After that, you are unlikely to use the bathroom for probably the next hour and a half, barring some sort of illness.

So, I propose that you use a log to track your bathroom habbits for a month. Just write down the time of each visit for a month, then we will be able to analyze the actual distribution of your visits. If it turns out that you have a predictable bladder, then the odds won't be so astronomical. Furthermore, maybe the "stalker" has similar predictability.
I heart Crystal Math.
matilda
Joined: Feb 4, 2010
• Posts: 317
August 16th, 2011 at 9:14:54 AM permalink
Quote: ChampagneFireball

But people don't go to the bathroom at random times. You don't have the same chance of going to the bathroom 5 minutes after the last trip as you do 90 minutes after.

In fact, if they have similar "P" cycles, if they met early in the day, the probability that they will meet again is high. If they drink their morning coffee or whatever at the same time and start work at the same time there is a higher probability that they will meet early in the morning. This would be true for every day of the week.
MathExtremist
Joined: Aug 31, 2010
• Posts: 6526
August 16th, 2011 at 9:59:37 AM permalink
Use a bathroom in a different part of the building exclusively for two weeks. If you run into that person the same number of times in spite of the change of scenery, either (a) they are stalking you or (b) they have a bladder condition.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
matilda
Joined: Feb 4, 2010
• Posts: 317
August 16th, 2011 at 10:15:32 AM permalink
It is assumed that you and he go 5 times a day. While you might know that you go 5 times a day, how can you assume he goes ONLY 5 times. Maybe he goes 100 times. Perhaps he is the rest room attendant.
SOOPOO
Joined: Aug 8, 2010