Question

If you flip a coin $10$ times, what are the odds that you will get the same number of heads and tails?

Answer 1

This is Binomial with $n=10$ and $p=0.5$ (assuming a fair coin)
Explanation:
Out of $10$ flips, the probability of getting $5$ heads (or tails) is...

$P(X=5)=\frac{10!}{5!\times 5!}\times {\left(\frac{1}{2}\right)}^5{\left(\frac{1}{2}\right)}^5=\frac{63}{256}\approx 0.246$
hope that helped