If Anita got \(\$ 500\) on her first punch, should she throw out her \(\$ 500\) and take the results of her second punch? How do you know?

The following exercise deal with the game "Punch a Bunch," which appears on the TV game show The Price Is Right. In this game, contestants have a chance to punch through up to 4 paper circles on a board; behind each circle is a card with a dollar amount printed on it. There are 50 of these circles; the dollar amounts are given in this table:

Contestants are shown their selected dollar amounts one at a time, in the order selected. After each is revealed, the contestant is given the option of taking that amount of money or throwing it away in favor of the next amount. (You can watch the game being played in the video Playing "Punch a Bunch." (https://openstax.org/r) Playing_Punch a _Bunch)) Anita is playing "Punch a Bunch” and gets 2 punches.

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Dollar Amount Frequency $25,000 1 $10,000 2 $5,000 4 $2,500 8 $1,000 $500 10 10 10 10 $250 10 10 $100 5