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Thread: 2 Stupid Questions? Can anyone do these?

  1. #1
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    Post Probability Questions.. HELPP Can someone PLZ do these?

    Dr Harve has found that 30 % of his clients have eye problems, 10 have hearing and 5 have both.. are an (eye problem and hearing problems) independent or dependent? why


    T.O Leafs is playing Montreal in Stanley cup finals. team to win 4 first wins the cup. If the prob of T.O winning (1) game is .55 determine the prob that
    a) T.O wins 4 straight
    b) Montreal wins the cup ( In general)
    Last edited by wikji; Mar 4th 2008 at 02:54 AM.
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  2. #2
    Junior Member roy_zhang's Avatar
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    Q.1
    First I guess you mean 10% and 5% instead of 10 and 5, am I right?
    If this is the case, we have $\displaystyle P(E)=0.3$, $\displaystyle P(H)=0.1$ and $\displaystyle P(E\cap H)=0.05$
    By definition, two events $\displaystyle A$ and $\displaystyle B$ are said to be independent if $\displaystyle P(A\cap B)=P(A)P(B)$.
    But here we have $\displaystyle P(E\cap H)=0.05$ and $\displaystyle P(E)P(H)=0.03$, hence they are dependent.

    Q.2
    First part is easy, just $\displaystyle P($wins 4 straight$\displaystyle )=(0.55)^4\approx 0.0915$;

    The second part deserves a little analysis, there are 4 cases a team can win the cup: (1) the team wins the 4th game in the 4th game in the series (this is the case of 4 straight wins as we found in part one); (2) the team wins the 4th game in the 5th game in the series; (3) the team wins the 4th game in the 6th game in the series;(4) the team wins the 4th game in the 7th game in the series. We need to sum all the four probabilities for these 4 cases, the second, third and fourth cases are follow exactly the negative binomial probability distribution (Check a reference for detail), so the probability for T.O. Leaf to win the series can be written as:

    $\displaystyle P(W) = P(1) + P(2) + P(3) + P(4)$ where $\displaystyle P(2)$ means the probability for case 2 above etc.

    $\displaystyle P(W) = (0.55)^4 + \binom{4}{3}(0.55)^4(0.45)^1 + \binom{5}{3}(0.55)^4(0.45)^2 + \binom{6}{3}(0.55)^4(0.45)^3 $
    $\displaystyle \approx 0.6083 $

    Thus the probability for Montreal to win will be $\displaystyle 1-P(W)\approx 0.3917$.
    Last edited by roy_zhang; Mar 5th 2008 at 08:45 AM.
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  3. #3
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    Quote Originally Posted by wikji View Post
    Dr Harve has found that 30 % of his clients have eye problems, 10 have hearing and 5 have both.. are an (eye problem and hearing
    T.O Leafs is playing Montreal in Stanley cup finals. team to win 4 first wins the cup. If the prob of T.O winning (1) game is .55 determine the prob that
    a) T.O wins 4 straight
    b) Montreal wins the cup ( In general)
    independant u don't c with ears and hear with eyes
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