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Math Help - Probability of attendance

  1. #1
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    Probability of attendance

    So there's this question I can't answer.

    Lets say I sell 50 tickets to an event. So that's 50 people that might attend this event.
    The chance of someone attending is 90%, how do I derive a formula to work out the probability of an x number of people attending.
    Say, I want to find out the chance of 30 people coming.
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  2. #2
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    Hello, deovolante!

    Lets say I sell 50 tickets to an event.
    So that's 50 people that might attend this event.
    The chance of someone attending is 90%.

    How do I derive a formula for the probability of x people attending?

    Say, I want to find out the chance of 30 people coming.

    This is a Binomial probability problem.

    . . \begin{array}{ccc}P(\text{attend}) &=& 0.9 \\ \\[-4mm] P(\sim\text{attend}) &=& 0.1 \end{array}


    \displaystyle{P(x\text{ attend}) \;=\;{50\choose x}(0.9)^x(0.1)^{50-x} }


    \displaystyle{P(\text{30 attend}) \;=\;{50\choose30}(0.9)^{30}(0.1)^{20}<br />
}

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, deovolante!


    This is a Binomial probability problem.

    . . \begin{array}{ccc}P(\text{attend}) &=& 0.9 \\ \\[-4mm] P(\sim\text{attend}) &=& 0.1 \end{array}


    \displaystyle{P(x\text{ attend}) \;=\;{50\choose x}(0.9)^x(0.1)^{50-x} }


    \displaystyle{P(\text{30 attend}) \;=\;{50\choose30}(0.9)^{30}(0.1)^{20}<br />
}

    what does the {50\choose x} represent?
    i mean, what do i put into my calculator?
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  4. #4
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    50\choose30 is the binomial combination formula. It is often labelled nCr on scientific calculators.

    If you dont have a scientific calculator: Binomial Coefficient Calculator
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  5. #5
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    Just a comment on Soroban's solution--

    This solution (the binomial distribution) assumes that each person's chances of attending is independent of other person's decisions to attend or not. If this is a "real-world" problem, that assumption is likely to be false. So proceed with caution.
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