I wrote about some probability calculations that I’d done on a whim. LK (that’s Anant without the ‘h’) says, on email that he thinks my calculations were wrong. He sent me this figure to make his point:
You should be able to check that the probability from that figure is closer to a third than to a sixth. This is proof positive that I was wrong, and that LK’s answer in the comments on the last post was right (although there still is no (120-t) in any denominator).
I am usually willing to be shown wrong, and to accept it when I am. Here, though, I couldn’t stop myself – out of disbelief, mostly – from writing my own test on MatLab, and re-doing the expression for the probability; correctly, this time.
Here, first, is the expression for the probability, in terms of ‘m’, the time I spend in the mess, and ‘n’, the time Avani spends in the mess. The first line simplifies to the second
The MatLab code I wrote is here, so you can check the results for yourself.
I’d averaged the second terms in each bracket as (m/2) and (n/2) respectively, the last time. Obviously, that’s the wrong thing to do. The expression above gives an answer that is close to, but not exactly, what LK got. The MatLab simulations also give similar probabilities. I can’t explain what is causing the discrepancy between the expression and LK’s vastly more understandable graph. Maybe LK will help.