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MATH / While staying in a 15-story hotel, Polya plays the following game. She enters an…

Problem

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problem

While staying in a 15-story hotel, Polya plays the following game. She enters an elevator on the 6th6^{\mathrm{th}} 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 7th7^{\mathrm{th}} floor or higher? Express your answer as a common fraction.
Plain-text mathematical notation (without MathML)
While staying in a 15-story hotel, Polya plays the following game. She enters an elevator on the 6^(th) 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 7^(th) floor or higher? Express your answer as a common fraction.
Original LaTeX notation
While staying in a 15-story hotel, Polya plays the following game. She enters an elevator on the $6^{\mathrm{th}}$ 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 $7^{\mathrm{th}}$ floor or higher? Express your answer as a common fraction.

level

Level 5

type

Counting & Probability

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Source and history

task_id
57630fd2-05e9-5eec-b46c-f7b86ccbb77f
task_key
counting~5fand~5fprobability--test--57630fd2-05e9-5eec-b46c-f7b86ccbb77f
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import