While staying in a 15-story hotel, Polya plays the following game. She enters an elevator on the $6th$ floor. She flips a fair coin five times to determine her next five stops. Each time she flips heads, she goes up one floor. Each time she flips tails, she goes down one floor. What is the probability that each of her next five stops is on the $7th$ floor or higher? Express your answer as a common fraction.
She will go up if she gets more heads than tails, and she will go down if she gets more tails than heads.
If when stops at the 7th floor or higher, that means she went up.
Since there's an equal chance of getting more heads than tails and getting more tails than heads, the answer is 1/2.