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!

Quote:rzervakos19A 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

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.

Quote:ChampagneFireballBut 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.