Determine how many times you must flip a fair coin so that:
The expected number of heads is 5.
One flip gives us \(\frac12\) head on average, so we must flip the coin ten times. (This follows from the linearity of expectation.)
The probability of at least 5 heads is \(\frac12\).
If we flip the coin nine times, then we can form pairs from the possible results by overturning all coins in a result set. In each pair one event will have at least 5 heads and the second will have fewer than five heads. So for this number of coins the probability of the required event and its complement are the same, so the probability is \(\frac12\).