A release-checked medium problem for training Expected Value, Games.
Question
You have $2$ indistinguishable urns in front of you. $$$$ The first urn has $4$ $(\$1$ chips) and $6$ $(\$10$ chips), while the second urn has $3$ $(\$1$ chips) and $7$ $(\$10$ chips). $$$$ You reach into one urn at random and select a $(\$1$ chip). Then you have the opportunity to pick another chip at random either from same urn you picked the first chip from or at random from the other urn. Your payout is the value of the second chip you select. Under optimal gameplay, what is your expected payout?
Practice focus
This Probability problem is tagged Expected Value, Games. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.