8. [5] Allison has a coin which comes up heads $\frac{2}{3}$ of the time. She flips it 5 times. What is the probability that she sees more heads than tails?
Answer: $\sqrt[64]{81}$ The probability of flipping more heads than tails is the probability of flipping 3 heads, 4 heads, or 5 heads. Since 5 flips will give $n$ heads with probability $\binom{5}{n}\left(\frac{2}{3}\right)^{n}\left(\frac{1}{3}\right)^{5-n}$, our answer is $\binom{5}{3}\left(\frac{2}{3}\right)^{3}\left(\frac{1}{3}\right)^{2}+\binom{5}{4}\left(\frac{2}{3}\right)^{4}\left(\frac{1}{3}\right)^{1}+\binom{5}{5}\left(\frac{2}{3}\right)^{5}\left(\frac{1}{3}\right)^{0}=\frac{64}{81}$.