Four matching coin tosses

Question

A fair coin is tossed four times. What is the probability that all four tosses come up the same?

Short answer

$\tfrac18$ . The first toss can be anything; each of the remaining three must match it, which happens with probability $(\tfrac12)^3=\tfrac18$ .

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Lessons behind this question

Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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