TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Levajkovic)/Übungen 2022W/HW01.2
Coin game[Bearbeiten | Quelltext bearbeiten]
Two players, A and B, alternately and independently flip a coin and the first player to obtain a head wins. Assume player A flips first.
Problem 5a)[Bearbeiten | Quelltext bearbeiten]
If the coin is fair, what is the probability that A wins?
Problem 5b)[Bearbeiten | Quelltext bearbeiten]
Suppose that , not necessarily . What is the probability that A wins?
Lösungsvorschlag von Friday[Bearbeiten | Quelltext bearbeiten]
--Friday Sa 30 Jan 2021 14:08:31 CET
Solution 5a)[Bearbeiten | Quelltext bearbeiten]
If describes the posibility that A winns and the winn of B, than we can create the following equation.
First we have the probability that A winns imideatly which is , or A loses at first but wins in one of the later rounds. This second part can be described with the probability that first A has to lose but in the end B has to lose the game. describes the probability that B will win the game.
So all we have to do now is to solve this equation:
Solution 5b)[Bearbeiten | Quelltext bearbeiten]
Let be the probability that A wins. A detailed description as how the equation gets created can be found at the problem at 5a).