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Math Help - Binomial distribution

  1. #1
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    Binomial distribution

    A bag contains 4 red, 5 blue and 6 green balls. The balls are indistinguishable except for their colour. A trial consists of drawing a ball at random from the bag, noting its colour and replacing it in the bag. A game is plated by performing 10 trials in all.

    At the start of the tournament, each player plays the above game once. Players who earned more than $k proceed to the next round. Find the least value of k such that, in a random sample of 10 players, the probability that all 10 players proceed to the next round is less than 0.1.

    Let X be the number of blue balls drew.

    X~B(10, \frac{1}{3})

    [P(X>n)]^{10} < 0.1 where n=\frac{k}{0.50}

    1-P(X n) <0.794

    P(X n) > 0.206
    Last edited by Punch; April 14th 2012 at 04:36 AM.
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  2. #2
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    Re: Binomial distribution

    Sorry! The missing part is: For each blue ball obtained, the player earns $0.50
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  3. #3
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    Re: Binomial distribution

    P(X=0)=0.01734 P(X=1)=0.0867 P(X=2)=0.1951 So P(X<or=2)= 0.01734+0.0867+0.1951=0.299

    So n=2 and k=1
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