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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?
 one year ago
 one year 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?
 one year ago
 one year ago

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experimentXBest ResponseYou've already chosen the best response.0
I don't seem to understand this problem ... are they allowed to come at any time?
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
Yes. 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.
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
\([0,T]\) is used to simplify.
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
and how long will I wait?
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
For example, 15 minutes = 1/4 hour.
 one year ago

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

klimenkovBest ResponseYou've already chosen the best response.1
If you are interested I will give you a solution.
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
But firstly, I'd like you to solve another problem.
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
hold on ... I'll wait.
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
If 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)?
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
Yes. 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
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
pir^2/4pir^2 = 1/4 ??
 one year ago

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

experimentXBest ResponseYou've already chosen the best response.0
all right ... let's get down to this.dw:1350223223318:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1350223247938:dw
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
Hint! 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 \((x,y)\).
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
No!!! The last one is wrong. Try to get why.
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
lol ... first one can arrive at any time ...it wouldn't matter.
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
They both can arrive at any time!
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1350223462963:dw
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
Better to say  you both :)
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
Hm.. Can't get what you do...
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
Lets come back to the shooter. What is the probability to hit in the center of the circle?
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
that is almost zero.
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
Not almost. It equals zero. Because the area of a point = 0.
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
The 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.
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
Oh. Any point of the SQUARE can show when this persons arrived.
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
What can you say now?
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
no ... just on it. let me try to understand it ...
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
For 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
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
how to represent waiting time then??
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
What about \(xy<\tau\) ?
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1350224492870:dw can it be independent of x?
 one year ago

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

experimentXBest ResponseYou've already chosen the best response.0
how to represent this probabilistically?
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
I 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.
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
So, what about x−y<τ ?
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
τ is not T right??
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
No. Find all points (x,y) that satisfy the statement of the problem.
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
\[ \piτ^2 \over T^2 \]
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
Where did you get pi?
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1350225916366:dw sorry .. kinda thought of complex number z < r
 one year ago

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

experimentXBest ResponseYou've already chosen the best response.0
yeah, is that correct?
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
dw:1350227268062:dw
 one year ago
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