# Binomial probability problem solving. The probability of sales representative making a sale with any one customer is 1/3. The sales representative makes eight contacts a day. To find the probability of making four sales, evaluate the term 8C_4(1/3)^4(2/4)^4

Binomial probability problem solving
The probability of sales representative making a sale with any one customer is $\frac{1}{3}$. The sales representative makes eight contacts a day. To find the probability of making four sales, evaluate the term
$8{C}_{4}\left(\frac{1}{3}{\right)}^{4}\left(\frac{2}{4}{\right)}^{4}$
In the expansion $\left(\frac{1}{3}+\frac{2}{3}{\right)}^{8}$
I know how to evaluate $8{C}_{4}\left(\frac{1}{3}{\right)}^{4}\left(\frac{2}{4}{\right)}^{4}$ but I don't understand what they mean by " in the expansion of $\left(\frac{1}{3}+\frac{2}{3}{\right)}^{8}$
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Step 1
The binomial theorem is that for variables a,b and positive integer exponent n, then we have the following.
$\left(a+b{\right)}^{n}=\sum _{k=0}^{n}{}^{n}{C}_{k}{a}^{k}{b}^{n-k}$
Since $1=\left(\frac{1}{3}+\frac{2}{3}{\right)}^{8}$, then the term for $k=4$ corresponds to the probability of 4 successes and 4 failures among 8 independent trials.
$1=\sum _{k=0}^{8}\mathsf{P}\left(X=k\right)$
Step 2
Therefore,
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