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Math Help - Finding Probability

  1. #1
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    Finding Probability

    In the Western Conference of the NHL there are 15 teams. Of those teams, three of them have 2 words in their name (St Louis, San Jose & Los Angeles). Each year eight of these teams qualify for the playoffs. Assume that all 15 teams have an equal chance of getting into the playoffs, what is the probabilty that

    a) none will make the playoffs

    b) at least one fo the teams will make the playoffs

    c) all the teams make the playoffs.



    To answer A would the correct way be to:
    Find how many possible ways the 8 teams could make the playoffs? Then subtract 3 out of there?

    C(15,8) = 259459200/40320 = 6435

    So There would be 6435 ways that only that only 8 of the 15 teams would make the playoffs

    Now how would I go about answer the probability that out of those 8 who make it, none of them are the three teams who have 2 words in their name??
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  2. #2
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    Re: Finding Probability

    Quote Originally Posted by momofmaxncoop View Post
    In the Western Conference of the NHL there are 15 teams. Of those teams, three of them have 2 words in their name (St Louis, San Jose & Los Angeles). Each year eight of these teams qualify for the playoffs. Assume that all 15 teams have an equal chance of getting into the playoffs, what is the probabilty that
    a) none will make the playoffs
    To answer A would the correct way be to:
    The answer A would the correct way:
    \frac{C(12,8)}{C(15,8)} WHY?
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  3. #3
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    Re: Finding Probability

    Because you are subtracting the 3 teams from the total amount of outcomes.

    so 2^15 =

    So would that be 11880/32768 =36.3%
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    Re: Finding Probability

    Quote Originally Posted by momofmaxncoop View Post
    Because you are subtracting the 3 teams from the total amount of outcomes.
    so 2^15 =
    So would that be 11880/32768 =36.3%
    2^{15} has absolutely nothing to do with anything.

    C(12,8)=495~\&~C(15,8)=6435.
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    Re: Finding Probability

    Thanks! I was just confusing myself with a similar question that is in my book.

    So B would be:
    C(13,8)
    C(15,8)

    Then C would be:
    C(15,8) ..correct??
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  6. #6
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    Re: Finding Probability

    Quote Originally Posted by momofmaxncoop View Post
    Thanks! I was just confusing myself with a similar question that is in my book.
    So B would be:
    C(13,8)
    C(15,8)

    Then C would be:
    C(15,8) ..correct??
    No none of that is correct.
    At least one is the complement of none.
    So the answer to b) is 1 minus the answer to a).

    For c) look at \frac{C(3,3)\cdot C(12,5)}{C(15,8)}
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