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.
For this, we can use a tree diagram for each coin flip.
For every H, add one to the total floor level. For every T, subtract one floor.
Count all the numbers in total. Then count all the numbers 6 or above.
39/62 Chance (or 62.9%) that she is above or at the 7th floor at any time during her game