Alice and Bob have 2n + 1 coins, each coin with probability of heads equal to 1/2. Bob tosses n + 1 coins, while Alice tosses the remaining n coins. Assuming independent coin tosses, show that the probability that after all coins have been tossed, Bob will have gotten more heads than Alice is 1/2.

Alice and Bob have 2n + 1 coins, each coin with probability of heads equal to 1/2. Bob tosses n + 1 coins, while Alice tosses the remaining n coins. Assuming independent coin tosses, show that the probability that after all coins have been tossed, Bob will have gotten more heads than Alice is 1/2.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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8. Alice and Bob have 2n + 1 coins, each coin with probability of heads equal to 1/2. Bob tosses n + 1
coins, while Alice tosses the remaining n coins. Assuming independent coin tosses, show that the
probability that after all coins have been tossed, Bob will have gotten more heads than Alice is 1/2.

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