You and I play the following game: I toss a coin repeatedly. The coin is not necessarily fair and P(H) = p ( the probability of getting a head is p) .The game ends the first time that two consecutive heads (HH) or two consecutive tails (TT) are observed. I win if (HH) is observed and you win if (TT) is observed. (a) Find the probability that I won the game. (b) Given that I won the game, find the probability that the first coin toss resulted in head. (c)If the game is fair, then p =?

You and I play the following game: I toss a coin repeatedly. The coin is not necessarily fair and P(H) = p ( the probability of getting a head is p) .The game ends the first time that two consecutive heads (HH) or two consecutive tails (TT) are observed. I win if (HH) is observed and you win if (TT) is observed. (a) Find the probability that I won the game. (b) Given that I won the game, find the probability that the first coin toss resulted in head. (c)If the game is fair, then p =?

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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(a) Find the probability that I won the game.

(b) Given that I won the game, find the probability that the first coin toss resulted in head.

(c)If the game is fair, then p =?

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