+ Reply to Thread
Page 1 of 2 1 2 LastLast
Results 1 to 15 of 18

Thread: I have a real stumper here

  1. #1
    Points: 403, Level: 8
    Level completed: 6%, Points required for next Level: 47

    Posts
    10
    Thanks
    5
    Thanked 0 Times in 0 Posts

    I have a real stumper here




    I have a question that has stumped everyone I have asked. I
    wonder if anyone can help. Here is the scenario.

    Every time that team A plays on Tuesday they win 8/10 or 80% of
    the time. Every time that team B plays on Tuesday they lose 6.6/10 or 66% of the time. This Tuesday they play each other, does the
    probability of team A winning increase and the probablity of
    team B losing increase?

    Many tried to say that you multiply, but in this case the
    situations are not independent, they are playing each other.

    Can you dig it!!!!!!!!!!!?????????????????//

  2. #2
    Points: 403, Level: 8
    Level completed: 6%, Points required for next Level: 47

    Posts
    10
    Thanks
    5
    Thanked 0 Times in 0 Posts

    Re: I have a real stumper here

    FYI this is not my homework. I am trying to find someone that can answer this question. I have asked several people in the so called math department in my district and everyone says let me get back to you on that. An answer would be greatly appreciated

  3. #3
    Ninja say what!?!
    Points: 8,297, Level: 61
    Level completed: 49%, Points required for next Level: 153
    Link's Avatar
    Posts
    1,165
    Thanks
    37
    Thanked 84 Times in 76 Posts

    Re: I have a real stumper here

    You're right in stating that the events are dependent on each other. If A wins, then B has to lose (and vice versa). However, you haven't given us enough information.

    You've said P(A=win | Tuesday) = .80 & P(B=win | Tuesday) = .34. To make this easier to explain, lets take the day out. Then P(A=win) = .80 and P(B=win) = .34.

    Now, what you're asking is for P(A|B). That is, what is the probability of team A winning given that they're playing team B? This can be found by:

    P(A|B) = P(A and B) / P(B)

    Likewise, P(B|A) = P(A and B) / P(A).

    You've given us P(A) and P(B). However, we don't know what P(A and B) is. Therefore, we can't find P(A|B).

  4. The Following User Says Thank You to Link For This Useful Post:

    HoldenRg (03-30-2012)

  5. #4
    Ninja say what!?!
    Points: 8,297, Level: 61
    Level completed: 49%, Points required for next Level: 153
    Link's Avatar
    Posts
    1,165
    Thanks
    37
    Thanked 84 Times in 76 Posts

    Re: I have a real stumper here

    btw.

    I can dig it.........

  6. The Following User Says Thank You to Link For This Useful Post:

    HoldenRg (03-30-2012)

  7. #5
    TS Contributor
    Points: 12,501, Level: 73
    Level completed: 13%, Points required for next Level: 349

    Posts
    951
    Thanks
    0
    Thanked 103 Times in 100 Posts

    Re: I have a real stumper here

    Hey Link, if that is indeed your real name, I was thinking that P(A and B) most likely = 0. Since they play on Tuesday, it cannot be American football. And most other American sports (baseball, basketball, American Idol) cannot end in a tie/two winners. Unless we're talking aboot hockey...

  8. #6
    Devorador de queso
    Points: 95,995, Level: 100
    Level completed: 0%, Points required for next Level: 0
    Awards:
    Posting AwardCommunity AwardDiscussion EnderFrequent Poster
    Dason's Avatar
    Location
    Tampa, FL
    Posts
    12,938
    Thanks
    307
    Thanked 2,630 Times in 2,246 Posts

    Re: I have a real stumper here

    Yeah I think there was some confusion when Link used B to refer both to "team B wins" and "the team that is being played against is team B".

  9. The Following User Says Thank You to Dason For This Useful Post:

    Link (02-10-2012)

  10. #7
    Ninja say what!?!
    Points: 8,297, Level: 61
    Level completed: 49%, Points required for next Level: 153
    Link's Avatar
    Posts
    1,165
    Thanks
    37
    Thanked 84 Times in 76 Posts

    Re: I have a real stumper here

    Quote Originally Posted by Dason View Post
    Yeah I think there was some confusion when Link used B to refer both to "team B wins" and "the team that is being played against is team B".
    LOL. Thank you for clarifying Dason.

  11. The Following User Says Thank You to Link For This Useful Post:

    HoldenRg (03-30-2012)

  12. #8
    Points: 403, Level: 8
    Level completed: 6%, Points required for next Level: 47

    Posts
    10
    Thanks
    5
    Thanked 0 Times in 0 Posts

    Re: I have a real stumper here

    So yeah I am not sure why I would take out Tuesday. There can't be a tie. So what I have come up with is combining both percentages and dividing them by 200. Gives the total percentage of one outcome. That is .80 + .66 = 1.4. Then 1.4 divided by 2= .73. Does this make sense to anyone or better yet can someone verify if this is right or wrong and why?

    Still trying to get this one

  13. #9
    Points: 403, Level: 8
    Level completed: 6%, Points required for next Level: 47

    Posts
    10
    Thanks
    5
    Thanked 0 Times in 0 Posts

    Re: I have a real stumper here

    Anyone? Anyone?

  14. #10
    Ninja say what!?!
    Points: 8,297, Level: 61
    Level completed: 49%, Points required for next Level: 153
    Link's Avatar
    Posts
    1,165
    Thanks
    37
    Thanked 84 Times in 76 Posts

    Re: I have a real stumper here

    Alright...I felt bad since no one was responding and will set up something formal and quick for you.

    Let's assume that: A|Tuesday ~ Ber(p=.80) and B|Tuesday ~ Ber(p=.66). Let Team A "win" if A=1 and B=0, Team B "win" if A=0 and B=1, and a rematch occur otherwise (on an identical Tuesday).

    Then P(Team A = "win") = P(A=1|Tuesday)*P(B=0|Tuesday) = (.80)*(.34) = .272
    P(Team B = "win") = P(A=0|Tuesday)*P(B=1|Tuesday) = (.20)*(.66) = .132
    P(Rematch) = (.80)*(.66) + (.20)*(.34) = .596

    Now, since rematches don't count towards the overall probability of teams A or B winning, we can drop it and just calculate based off the prior two probabilities. This results in an "overall" P(Team A wins) = .272/(.272 + .132) = .67 and P(Team B wins) = .132/(.272 + .132) = .33.

    HTH.

  15. The Following User Says Thank You to Link For This Useful Post:

    HoldenRg (03-30-2012)

  16. #11
    Ninja say what!?!
    Points: 8,297, Level: 61
    Level completed: 49%, Points required for next Level: 153
    Link's Avatar
    Posts
    1,165
    Thanks
    37
    Thanked 84 Times in 76 Posts

    Re: I have a real stumper here

    please note that this approaches the problem with an independence and stochastic assumption (i.e. that it doesn't matter who team A plays...it could be team C, D, E, etc. and that there is randomness (no skill involved)).

  17. The Following User Says Thank You to Link For This Useful Post:

    HoldenRg (02-25-2012)

  18. #12
    Points: 403, Level: 8
    Level completed: 6%, Points required for next Level: 47

    Posts
    10
    Thanks
    5
    Thanked 0 Times in 0 Posts

    Re: I have a real stumper here

    I am still a bit unsure but this is the best answer I have received yet. I appreciate it.

  19. #13
    Points: 403, Level: 8
    Level completed: 6%, Points required for next Level: 47

    Posts
    10
    Thanks
    5
    Thanked 0 Times in 0 Posts

    Re: I have a real stumper here

    Thanks Link!!! So was my approach totally off or was I at least in the same area code of being right?

  20. #14
    Points: 403, Level: 8
    Level completed: 6%, Points required for next Level: 47

    Posts
    10
    Thanks
    5
    Thanked 0 Times in 0 Posts

    Re: I have a real stumper here

    By unsure I mean about my understanding not your answer Link

    I hope I did not disrespect

  21. #15
    Points: 403, Level: 8
    Level completed: 6%, Points required for next Level: 47

    Posts
    10
    Thanks
    5
    Thanked 0 Times in 0 Posts

    Re: I have a real stumper here


    I think I was a bit close all of my results seem to be about ten percent lower that than those of this formula. Interesting. Any more input is greatly appreciated

+ Reply to Thread
Page 1 of 2 1 2 LastLast

           




Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats