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Thread: New to Binomial and Probability

  1. #1
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    New to Binomial and Probability

    Hi everyone,

    Im new to all this. I have been spending alot of time these past few days doing various things related to Stats etc.

    Im trying to understand, but its hard for me and I need help understanding. Here is a question;

    Assume a binomial experiment in the following questions. Find the probability;
    a) of exactly 5 successes, where n=7 and p=0.5
    b) of between 8 and 12 successes, where n=15 and p=0.7
    c) of at least 8 successes, where n=12 and p=0.5

    Being so new I am having a hard time with this. Any help?

    Duey
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Duey View Post
    Hi everyone,

    Im new to all this. I have been spending alot of time these past few days doing various things related to Stats etc.

    Im trying to understand, but its hard for me and I need help understanding. Here is a question;

    Assume a binomial experiment in the following questions. Find the probability;
    a) of exactly 5 successes, where n=7 and p=0.5
    b) of between 8 and 12 successes, where n=15 and p=0.7
    c) of at least 8 successes, where n=12 and p=0.5

    Being so new I am having a hard time with this. Any help?

    Duey
    for the binomial distribution $\displaystyle B(N,p)$, the probability of exactly $\displaystyle n$ successes from $\displaystyle N$ and individual case probability of success $\displaystyle p$ is:

    $\displaystyle
    p(n; N, p)=\frac{N!}{n!(N-n)!}p^n(1-p)^{N-n}
    $

    for part a sunbstitue in the given values.

    for part b (assuming it is between 8 and 12 successes inclusive):

    $\displaystyle
    p(8,15,0.7)+p(9,15,0.7)+p(10,15,0.7)+p(11,15,0.7)+ p(12,15,0.7)
    $

    for part c:

    $\displaystyle
    p(8,12,0.5)+p(9,12,0.5)+p(10,12,0.5)+p(11,12,0.5)+ p(12,12,0.5)
    $

    That is you sum the probabilities for the case3s included by the condition

    RonL
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  3. #3
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    The trouble im having is doing the actual fomula, some of it i understand, some of it i don't. Looking for step by step instructions to show me so I can actually understand it.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Duey View Post
    The trouble im having is doing the actual fomula, some of it i understand, some of it i don't. Looking for step by step instructions to show me so I can actually understand it.
    i'll show you how to do the first, the rest are similar:

    In the Binomial distribution we have that, the probability of $\displaystyle k$ successes in $\displaystyle n$ trials is given by:

    $\displaystyle P(k) = {n \choose k}p^kq^{n-k}$

    where $\displaystyle p$ is the probability of success, and $\displaystyle q = 1 - p$ is the probability of failure.

    In this question, $\displaystyle n = 7, ~p = q = 0.5$

    we want P(5) ...exactly 5 successes

    thus, $\displaystyle P(5) = {7 \choose 5} \left( \frac 12 \right)^5 \left( \frac 12 \right)^2 = 21 \cdot \frac 1{32} \cdot \frac 14 = \frac {21}{128}$



    for (b), between 8 and 12 successes (inclusive)

    we want $\displaystyle P(8 \le k \le 12) = P(8) + P(9) + P(10) + P(11) + P(12)$

    find each as i did the one above and sum them. here n = 15, p = 0.7, q = 0.3



    for (c), we want the probability of 8 or more successes.

    that is, $\displaystyle P(k \ge 8) = P(8) + P(9) + P(10) + P(11) + P(12)$

    here, n = 12, p = q = 0.5
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