Answered: Three fair coins are tossed…

Three fair coins are tossed simultaneously until all three show that same face. What is the probability that they are tossed more than three times?

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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Question

Three fair coins are tossed simultaneously until all three show that same face. What is the probability that they are tossed more than three times?

Is my answer correct?

Under geometric distribution: P(X>=t) = (1-p)^t; t=number of failures before first success

All the possible outcomes in one toss: HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

p=P(all three coins are the same face in one toss) = 2/8 = 1/4

Toss 1: Fail, Toss 2: Fail, Toss 3: Fail, Toss 4: Success

P(X>=3) = (1-1/4)³= 0.421875

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