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Thread: Discrete Binomial Probability Distributions Questions

  1. #1
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    Discrete Binomial Probability Distributions Questions

    Hi everyone,

    I can't seem to get the answers to these questions.

    a) Four marbles are in a jar, with the values 0, 1, 10 and 100 printed on them. Push-up Pete will draw a marble each morning and do that many push-ups. What is the probability that he will draw the “100” marble exactly 2 times in a week

    b) Four marbles are in a jar, with the values 0, 1, 10 and 100 printed on them. Push-up Pete will draw a marble each morning and do that many push-ups. What is the probability that he won’t have to do push-ups for exactly one week (7 days in a row)

    For a) I tried

    P(2)=4Cnr2*(1/4)^2*(3/4)^2
    =27/128

    but this doesn't seem to work.

    I'm not exactly sure where to start with b)

    Thanks!


    Last edited by jugglingbubbles; Oct 24th 2018 at 04:36 PM.
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  2. #2
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    Re: Discrete Binomial Probability Distributions Questions

    $p=P[100] = \dfrac 1 4$

    $n=7$

    $P[\text{2 100s in a week}]= \dbinom{7}{2} \left(\dfrac 1 4\right)^2~\left(1-\dfrac 1 4\right)^{7-2} =$

    $21\cdot \dfrac{1}{16}\dfrac{243}{1024} =\dfrac{5103}{16384}$

    $P[\text{no pushups in 7 days}] = P[\text{draw 0 7 days consecutively}] = \left(\dfrac 1 4 \right)^7 = \dfrac{1}{16384}$
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  3. #3
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    Re: Discrete Binomial Probability Distributions Questions

    Quote Originally Posted by jugglingbubbles View Post
    Four marbles are in a jar, with the values 0, 1, 10 and 100 printed on them. Push-up Pete will draw a marble each morning and do that many push-ups. What is the probability that he will draw the 100 marble exactly 2 times in a week
    Here is another question. What is the probability that Pete will do exactly $141$ push-ups in one week?
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  4. #4
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    Re: Discrete Binomial Probability Distributions Questions

    And what is the probability that Pete will survive the week!
    Thanks from Plato and topsquark
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