# What is the probability of getting 7 heads and 7 tails with 14 coin flips?

$\left(\begin{matrix}14 \\ 7\end{matrix}\right) {\left(\frac{1}{2}\right)}^{7} {\left(\frac{1}{2}\right)}^{7} = 3432 \left(0.0078125\right) \left(0.0078125\right) \approx 0.2095$

#### Explanation:

The probability of getting a heads on any given flip is $\frac{1}{2}$. Same with the probability of getting tails on any given flip. The las thing we need to know is the number of ways we can order the Heads and Tails results - and that's $\left(\begin{matrix}14 \\ 7\end{matrix}\right)$. Overall, we have:

$\left(\begin{matrix}14 \\ 7\end{matrix}\right) {\left(\frac{1}{2}\right)}^{7} {\left(\frac{1}{2}\right)}^{7} = 3432 \left(0.0078125\right) \left(0.0078125\right) \approx 0.2095$