Question

In a game a player draws and replaces a card from a deck 2 times. The possible outcomes and payouts are shown. What is the

Answer 1

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

$EV=(\frac{26}{52})(\ 20)+(\frac{52}{52})(\ 4)+(\frac{52}{52})(\ 0)+(\frac{26}{52})(-\ 12)$

Simplifying the values, we have;

$EV=(\frac{1}{2})(\ 20)+(1)(\ 4)+(1)(\ 0)+(\frac{1}{2})(-\ 12)$

Dividing the terms, we get;

$EV=\ 10+\ 4+\ 0+-\ 6$

Adding, we have;

$EV=\ 8$

Thus, the expected value for someone playing the game is $8