Probability of 2 people meeting at given times

In summary, haru suggests that one should imagine a rectangular grid on which one can place representations of Alice and Bob, and then calculate the intersection points. He gives an example of how to do this for a problem with two people, and suggests that for a problem with more than two people, one should use a different approach.
  • #1
pugtm
18
0

Homework Statement


i'm having trouble coming up with an equation for this problem
[/B]
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.

Homework Equations


that is the question

The Attempt at a Solution



p =time^2-(1-t1)^2/2-(1-t2)^2/2[/B]
as time goes up exponentially the probability increases. as it does if their individual times increase.
 
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  • #2
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
Hi pug,
could you elaborate how you found your probability ?
pugtm said:
p =time^2-(1-t1)^2/2-(1-t2)^2/2
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 !
 

Related to Probability of 2 people meeting at given times

1. What is the probability of two people meeting at a specific time?

The probability of two people meeting at a specific time depends on several factors such as the population size, the location, and the probability of each person being at that location at that specific time. It can vary widely and is difficult to determine without more specific information.

2. How is the probability of two people meeting at a given time calculated?

The probability of two people meeting at a given time can be calculated by dividing the number of times they have met by the total number of times they had the opportunity to meet. This is known as the frequency method and is based on past occurrences.

3. Can the probability of two people meeting at a given time be predicted?

While it is possible to estimate the probability of two people meeting at a given time based on past occurrences and other factors, it is not possible to predict with certainty whether or not they will actually meet. There are too many variables at play to accurately predict this outcome.

4. What are some factors that can affect the probability of two people meeting at a given time?

Some factors that can affect the probability of two people meeting at a given time include their schedules, the locations they frequent, and their proximity to each other. Other factors such as chance encounters or mutual friends may also play a role.

5. Is the probability of two people meeting at a given time affected by their relationship?

The probability of two people meeting at a given time can be affected by their relationship, as people are more likely to meet if they have a mutual connection or if they share similar interests and habits. However, this is not always the case and other factors may have a greater influence on the probability of them meeting.

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