Given:
Given that in a game a player draws and replaces a card from a deck 2 times.
The possible outcomes and payouts are given.
We need to determine the expected value for someone playing the game.
Expected value:
The expected value for someone playing the game can be determined by
[tex]EV=(\frac{26}{52})(\$ 20)+(\frac{52}{52})(\$4)+(\frac{52}{52})(\$ 0)+(\frac{26}{52})(-\$12)[/tex]
Simplifying the values, we have;
[tex]EV=(\frac{1}{2})(\$ 20)+(1)(\$4)+(1)(\$ 0)+(\frac{1}{2})(-\$12)[/tex]
Dividing the terms, we get;
[tex]EV=\$ 10+\$4+\$ 0+-\$6[/tex]
Adding, we have;
[tex]EV=\$ 8[/tex]
Thus, the expected value for someone playing the game is $8
