1. [5] If five fair coins are flipped simultaneously, what is the probability that at least three of them show heads?
Answer: $\square$
The coin either lands heads-up at least three times or lands heads-down at least three times. These scenarios are symmetric so the probably is just $\frac{1}{2}$.
Alternatively, we can explicitly compute the probability, which is just $\frac{\binom{5}{3}+\binom{5}{4}+\binom{5}{5}}{1}=\frac{16}{32}=\frac{1}{2}$