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 2 years ago
Two persons want to meet. They know the place where to meet. The time when one of them come to the place of meeting is equiprobable and lies in the \([0,T]\). Someone of them who comes first will wait \(\tau\) minutes and go away. What is the probability of meeting?
 2 years ago
Two persons want to meet. They know the place where to meet. The time when one of them come to the place of meeting is equiprobable and lies in the \([0,T]\). Someone of them who comes first will wait \(\tau\) minutes and go away. What is the probability of meeting?

This Question is Closed

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0I don't seem to understand this problem ... are they allowed to come at any time?

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1Yes. Any time from 0 to T. For example you want to meet your friend between 1 p.m and 2 p.m. This is the same.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1\([0,T]\) is used to simplify.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0and how long will I wait?

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1For example, 15 minutes = 1/4 hour.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0I'm not good with probability ... but this question seems interesting ... since most of my friends always like about time and distance while waiting.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1If you are interested I will give you a solution.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1But firstly, I'd like you to solve another problem.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0hold on ... I'll wait.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1If there are n balls in the very dark room and among them are m white and other nm are black. What is the probability to take a white ball if you can see nothing and the probabilities for taking any of n balls are the same (equiprobable)?

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1Yes. Now lets try more complicated what is called a geometric probability. Someone want to hit the zone #1 by shooting from a gun. What is the probability to shot at zone #1 if the shooter always hit in the big circle? dw:1350222646524:dw

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0pir^2/4pir^2 = 1/4 ??

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1Yes. Very good! So the probability is the ratio of the areas! The method for my problem is very similar.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0all right ... let's get down to this.dw:1350223223318:dw

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1350223247938:dw

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1Hint! Let x is the time for the first person for example  for you. And y is for the second one  your friend. So the situation when you will come can be described as the pair \((x,y)\).

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1No!!! The last one is wrong. Try to get why.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0lol ... first one can arrive at any time ...it wouldn't matter.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1They both can arrive at any time!

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1350223462963:dw

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1Better to say  you both :)

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1Hm.. Can't get what you do...

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1Lets come back to the shooter. What is the probability to hit in the center of the circle?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0that is almost zero.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1Not almost. It equals zero. Because the area of a point = 0.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1The same situation is here. The pair of (x,y) describes the situation. So there will be a square.dw:1350223775014:dw Any point of this circle can show when this persons arrived. Like the shot in any point of the circle.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1Oh. Any point of the SQUARE can show when this persons arrived.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1What can you say now?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0no ... just on it. let me try to understand it ...

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1For example, you decided to meet you friend near restaurant between 14:00 and 14:30. You can arrive at any time between 14 and 14:30 the same situation for him. Let sign the time when you arrive with x and his time  y. For example you arrives at 14:09 and he at 14:29. This will be the point dw:1350224152495:dw

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0how to represent waiting time then??

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1What about \(xy<\tau\) ?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1350224492870:dw can it be independent of x?

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1In my example if \(\tau=21 \) min you will meet your friend. But if \(\tau < 20\) you will not.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0how to represent this probabilistically?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0I thought, if first person comes after time x and waits time t then the probability is \[ {t \over Tx}\] but this is not independent of x.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1So, what about x−y<τ ?

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1No. Find all points (x,y) that satisfy the statement of the problem.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0\[ \piτ^2 \over T^2 \]

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1Where did you get pi?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1350225916366:dw sorry .. kinda thought of complex number z < r

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1The condition that they will meet is \(x=y<\tau\). Got it?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0yeah, is that correct?

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1350227268062:dw
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