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Math Help - NCAA Probabilty Problem: HELP!!!!!!!

  1. #1
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    NCAA Probabilty Problem: HELP!!!!!!!

    Hello,

    I am taking a statistics class and my professor gave us an extra credit problem about the NCAA. He said we could "talk to anyone," so if you wouldn't mind helping me, I'd appreciate it so that I can understand the problem, get the answer right, and hopefully maintain my 4.0 GPA...


    Sixteen teams will make the "Sweet 16" round of the NCAA Basketball Tournament. The teams are denoted at T1, T2,...T16, where T1, T2 play and T3, T4 play, and the winners go on to the "Elite 8," then the "Final 4," and then the National Championship. (This is a single elminination tournament). If you choose at random the winners of the Sweet 16 round and, from those winners choose at random the winners of the Elite 8 round, from those winners choose at random the winners of the Final 4 round and form those winners choose at random the winner of the National Championchip, what is the probablity that you would have picked the entire tournamente correctly? Interpret "choose at random the winner" to mean that you have a probabilty of 0.5 of choosing the winning team for each game played.


    --I talked to my professor after class. He said that basically it's asking that with single elimination, what is the probability of choosing all the winners for all the matches correctly.



    Thank you IMMENSLY!!!!
    kcck
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  2. #2
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    Quote Originally Posted by Kcck View Post
    Hello,

    I am taking a statistics class and my professor gave us an extra credit problem about the NCAA. He said we could "talk to anyone," so if you wouldn't mind helping me, I'd appreciate it so that I can understand the problem, get the answer right, and hopefully maintain my 4.0 GPA...


    Sixteen teams will make the "Sweet 16" round of the NCAA Basketball Tournament. The teams are denoted at T1, T2,...T16, where T1, T2 play and T3, T4 play, and the winners go on to the "Elite 8," then the "Final 4," and then the National Championship. (This is a single elminination tournament). If you choose at random the winners of the Sweet 16 round and, from those winners choose at random the winners of the Elite 8 round, from those winners choose at random the winners of the Final 4 round and form those winners choose at random the winner of the National Championchip, what is the probablity that you would have picked the entire tournamente correctly? Interpret "choose at random the winner" to mean that you have a probabilty of 0.5 of choosing the winning team for each game played.


    --I talked to my professor after class. He said that basically it's asking that with single elimination, what is the probability of choosing all the winners for all the matches correctly.



    Thank you IMMENSLY!!!!
    kcck

    There are 15 games which you have to select the winner, each selection has
    a 0.5 probability of success.

    RonL
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  3. #3
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    so then would I do (0.5)^15 (one half to the fifteenth power)???
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    Quote Originally Posted by Kcck View Post
    so then would I do (0.5)^15 (one half to the fifteenth power)???
    Yes, unless I've missed something

    RonL
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    thanks ALOT!!! That's what I was going to do in the first place.

    However...

    i found this other site, and this guy seems to be doing something completely different...

    Math Forum - Ask Dr. Math
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    Quote Originally Posted by Kcck View Post
    thanks ALOT!!! That's what I was going to do in the first place.

    However...

    i found this other site, and this guy seems to be doing something completely different...

    Math Forum - Ask Dr. Math
    No its very convoluted but will give the same result (except for there being
    63 games).

    RonL
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    15 games? How are you getting 15 games?
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  8. #8
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    Quote Originally Posted by Kcck View Post
    15 games? How are you getting 15 games?
    The way I read your question there are 16 teams, as in each game one team
    loses and is knocked out, there are 15 losers altogether, and so there must
    be 15 games in the tournament.

    If you mean there is some other number of teams N say, then there are N-1
    games in a knockout tounament.

    RonL
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  9. #9
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    Quote Originally Posted by Kcck View Post
    Hello,

    I am taking a statistics class and my professor gave us an extra credit problem about the NCAA. He said we could "talk to anyone," so if you wouldn't mind helping me, I'd appreciate it so that I can understand the problem, get the answer right, and hopefully maintain my 4.0 GPA...


    Sixteen teams will make the "Sweet 16" round of the NCAA Basketball Tournament. The teams are denoted at T1, T2,...T16, where T1, T2 play and T3, T4 play, and the winners go on to the "Elite 8," then the "Final 4," and then the National Championship. (This is a single elminination tournament). If you choose at random the winners of the Sweet 16 round and, from those winners choose at random the winners of the Elite 8 round, from those winners choose at random the winners of the Final 4 round and form those winners choose at random the winner of the National Championchip, what is the probablity that you would have picked the entire tournamente correctly? Interpret "choose at random the winner" to mean that you have a probabilty of 0.5 of choosing the winning team for each game played.


    --I talked to my professor after class. He said that basically it's asking that with single elimination, what is the probability of choosing all the winners for all the matches correctly.



    Thank you IMMENSLY!!!!
    kcck
    Well, to choose the winners of the 8 games in the Sweet 16, so:
    0.5^8

    Now, you must be correct on the 4 games in the Elite 8, so:
    0.5^4

    Next, you must be right about both Final Four games, so:
    0.5^2

    Lastly, you must be right about the Championship, so:
    0.5

    The product of these four answers is your grand answer, so:
    0.5^8 * 0.5^4 * 0.5^2 * 0.5

    0.5^{15}

    See how that is 15 games?

    \frac{1}{2^{15}}

    0.000030518

    .0030518%
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