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Probability of 2 people meeting at given times

  1. Jan 5, 2017 #1
    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. jcsd
  3. Jan 5, 2017 #2

    haruspex

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    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.
     
  4. Jan 5, 2017 #3

    BvU

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    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 :smile:) 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 !
     
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