A release-checked easy problem for training Games, Expected Value, Conditional Probability.
Question
There are four balls, two black and two yellow, in a box. You pick out one at a time at random without replacement. Before picking each one out, you guess at the color, and if you're right, you receive in dollars the number of balls left in the container before you chose it. For example, if you guess the first ball correctly, you would receive $\$4$ because there were 4 balls remaining in the box before you picked one out. Assuming optimal play, what is the expected payoff for this game?
Practice focus
This Brainteasers problem is tagged Games, Expected Value, Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.