Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

klimenkov

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

  • This Question is Closed
  1. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't seem to understand this problem ... are they allowed to come at any time?

    • one year ago
  2. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 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
  3. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    \([0,T]\) is used to simplify.

    • one year ago
  4. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    and how long will I wait?

    • one year ago
  5. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    For example, 15 minutes = 1/4 hour.

    • one year ago
  6. experimentX
    Best Response
    You've already chosen the best response.
    Medals 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
  7. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    If you are interested I will give you a solution.

    • one year ago
  8. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    But firstly, I'd like you to solve another problem.

    • one year ago
  9. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    hold on ... I'll wait.

    • one year ago
  10. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    If there are n balls in the very dark room and among them are m white and other n-m 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
  11. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    m/n??

    • one year ago
  12. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 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
  13. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    pir^2/4pir^2 = 1/4 ??

    • one year ago
  14. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes. Very good! So the probability is the ratio of the areas! The method for my problem is very similar.

    • one year ago
  15. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    all right ... let's get down to this.|dw:1350223223318:dw|

    • one year ago
  16. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1350223247938:dw|

    • one year ago
  17. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 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
  18. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    No!!! The last one is wrong. Try to get why.

    • one year ago
  19. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    lol ... first one can arrive at any time ...it wouldn't matter.

    • one year ago
  20. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    They both can arrive at any time!

    • one year ago
  21. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1350223462963:dw|

    • one year ago
  22. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    Better to say - you both :)

    • one year ago
  23. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    Hm.. Can't get what you do...

    • one year ago
  24. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    Lets come back to the shooter. What is the probability to hit in the center of the circle?

    • one year ago
  25. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    that is almost zero.

    • one year ago
  26. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    Not almost. It equals zero. Because the area of a point = 0.

    • one year ago
  27. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    haha ..

    • one year ago
  28. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 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
  29. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh. Any point of the SQUARE can show when this persons arrived.

    • one year ago
  30. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    What can you say now?

    • one year ago
  31. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    Did you get it?

    • one year ago
  32. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    no ... just on it. let me try to understand it ...

    • one year ago
  33. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 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
  34. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    how to represent waiting time then??

    • one year ago
  35. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    What about \(|x-y|<\tau\) ?

    • one year ago
  36. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1350224492870:dw| can it be independent of x?

    • one year ago
  37. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    In my example if \(\tau=21 \) min you will meet your friend. But if \(\tau < 20\) you will not.

    • one year ago
  38. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    how to represent this probabilistically?

    • one year ago
  39. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    I thought, if first person comes after time x and waits time t then the probability is \[ {t \over T-x}\] but this is not independent of x.

    • one year ago
  40. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    So, what about |x−y|<τ ?

    • one year ago
  41. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    τ is not T right??

    • one year ago
  42. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    Sure!

    • one year ago
  43. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    is it (τ /T) ?

    • one year ago
  44. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    No. Find all points (x,y) that satisfy the statement of the problem.

    • one year ago
  45. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    pi t^2/T^2 ??

    • one year ago
  46. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    \[ \piτ^2 \over T^2 \]

    • one year ago
  47. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    Where did you get pi?

    • one year ago
  48. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1350225916366:dw| sorry .. kinda thought of complex number |z| < r

    • one year ago
  49. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    The condition that they will meet is \(|x=y|<\tau\). Got it?

    • one year ago
  50. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    |x−y|<τ

    • one year ago
  51. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah, is that correct?

    • one year ago
  52. klimenkov
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1350227268062:dw|

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.