medium Probability
A release-checked medium problem for training Games, Expected Value, Bernoulli/Binomial, Coins.
4 fair coins are laid out in front of you and are flipped. You receive the amount of dollars equal to the number of heads that appear. However, you also have the option to re-flip all 4 coins at once one time for $\$1$. If you re-flip whenever you get $0$ or $1$ heads on the initial flip, what is the fair value of this game?
This Probability problem is tagged Games, Expected Value, Bernoulli/Binomial, Coins. 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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