One of two blue dice matching a red die

Question

You roll one red and two blue fair six-sided dice. What is the probability that exactly one of the blue dice shows the same number as the red die?

Short answer

$\tfrac5{18}$ . Whatever the red die shows, each blue die matches it independently with probability $\tfrac16$ . Exactly one match among the two is a binomial event: $2\cdot\tfrac16\cdot\tfrac56=\tfrac{5}{18}$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Counting and Combinatorics
Expectation, Mean, and Variance
Sample Spaces, Events, and the Probability Axioms

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