1. ## 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.

2. 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.

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

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

$\displaystyle{P(\text{30 attend}) \;=\;{50\choose30}(0.9)^{30}(0.1)^{20}
}$

3. Originally Posted by Soroban
Hello, deovolante!

This is a Binomial probability problem.

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

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

$\displaystyle{P(\text{30 attend}) \;=\;{50\choose30}(0.9)^{30}(0.1)^{20}
}$

what does the ${50\choose x}$ represent?
i mean, what do i put into my calculator?

4. $50\choose30$ is the binomial combination formula. It is often labelled nCr on scientific calculators.

If you dont have a scientific calculator: Binomial Coefficient Calculator

5. 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.