# Probability of 2 people meeting at given times

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1. Jan 5, 2017

### pugtm

1. The problem statement, all variables and given/known data
i'm having trouble coming up with an equation for this problem

Mulder and Scully agree to meet at the FBI lobby sometime within a period of N minutes (e.g. 40 minutes).
Each of them may show up anytime during that period (with a uniform distribution).
If Scully arrives and Mulder isn't there, she will wait for X minutes and then leave.
If Mulder arrives and Scully isn't there, he will wait for Y minutes and then leave.
Neither of them waits beyond the end of the N minutes period.
Write a function that gets , N X and Y and computes the probability that Alice and Bob meet. The
function's inputs will be:...

Plot your result for X=5, Y=7, 10<=N<=60.

2. Relevant equations
that is the question

3. The attempt at a solution

p =time^2-(1-t1)^2/2-(1-t2)^2/2

as time goes up exponentially the probability increases. as it does if their individual times increase.

2. Jan 5, 2017

### haruspex

It will probably be easiest to use a graphical approach. Consider the arrival times, Tx and Ty, as coordinates. Diagrammatically, what represents their meeting?
I would break it into separate cases according to whether Tx+X<N, etc.

3. Jan 5, 2017

### BvU

Hi pug,
could you elaborate how you found your probability ?
In particular: how do you ensure it represents a probability at all (namely $\int = 1$ and: dimensionless -- none of these I recognize)

Also: I don't see what t, t1 and t2 represent (but I can guess)

Then: Expanding on haru's advice: pick a value for N, say 21 (the width of an A4 in cm ) let a 5 cm wide rectangle of paper or cardboard represent Fox (there are no Alice and Bob in the problem statement description!) and a 7 cm wide one represent Dana. Shift left and right and discover !