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Mystery Die

A release-checked easy problem for training Expected Value/LOTUS, Dice.

Question

You have a fair 18-face die where each side can either be a $4$ or a $2$. If the expected value of each die roll is $\frac{8}{3}$, how many $2$s are on the die?

Practice focus

This Brainteasers problem is tagged Expected Value/LOTUS, Dice. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.

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Brainteasers · Marshall Wace, Akuna