For sake of simplicity, let us assume that you have won exactly three punches for the game AND that no
prizes are removed after each punch. You are then shown the punching board, which contains 50 slots
with the following dollar amounts: (5) $100, (10) $250, (10) $500, (10) $1000, (8) $2500, (4) $5000, (2)
$10000, (1) $25000. You get to punch one slot at a time and either keep the amount you found or
continue with your other punches.
Working backwards, if you have already used and thrown away your first two punches, there is no
strategy for the third punch. You take whatever you get. Now examine the second punch.
QUESTION 1: What is the expected value of your third punch? Again, for sake of simplicity, assume that
your first two punches were put back into the mix. (Essentially no prizes are removed so there are still
50 holes to punch) Show all calculations necessary for you answer.
Also the question in the picture