# Thread: probability of rolling a die

1. ## probability of rolling a die

A casino game has the following rules: roll a fair six-sided die once. If you roll a 1, you get $12. If you roll a 3, you get$3. If you roll any other number, you lose $1. if u were running a casino, would u want this game there? why or why not? 2. Originally Posted by imverystupid A casino game has the following rules: roll a fair six-sided die once. If you roll a 1, you get$12. If you roll a 3, you get $3. If you roll any other number, you lose$1.

if u were running a casino, would u want this game there? why or why not?

We should compute expected value, if the casino comes out positive, you would want the game

So,

P(rolling a 1) $=\frac{1}{6}$
P(rolling a 3) $=\frac{1}{6}$
P(rolling 2 or 4 or 5 or 6) $=\frac{4}{6}$

Expected value=P(rolling a 1)*($won by rolling a 1)+P(rolling a 3)*($ won by rolling a 3)+P(rolling 2 or 4 or 5 or 6)*(\$ won by rolling a 2 or 4 or 5 or 6)

$=\frac{1}{6}(12)+\frac{1}{6}(3)+\frac{4}{6}(-4)=2+.5-2-\frac{2}{3}=\frac{1}{2}-\frac{2}{3}$

This is a negative number. So if you play this game you will lose money over the long run. So a casino would be happy to have this game