Odd head count from a hundred coins

Question

One hundred fair coins are tossed together. What is the probability that the number of heads is odd?

Short answer

$1/2$ . Whatever happens with the first $99$ coins, the last coin makes the total odd with probability exactly $1/2$ .

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Lessons behind this question

Conditional Probability, Total Probability, and Bayes' Rule
Worked Examples — Probability Trees, Monty Hall, and Bayesian Updating
Sample Spaces, Events, and the Probability Axioms

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