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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 seven stops is on the 7th floor or higher? Express your answer as a common fraction.

 Oct 27, 2020
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If she flips four heads out of the seven, she is guaranteed to be on the 7th floor or above.

 

Since it is 1/2 chance to flip heads:

1/2 x 1/2 x 1/2 x 1/2 = 1/16

1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/32

1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/64

1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/128

 

1/16 + 1/32 + 1/64 + 1/128 = 15/128

 

So, I believe the probability of her being on the 7th floor or above : 15/128.

 Feb 5, 2021

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