Wednesday

July 23, 2014

July 23, 2014

Posted by **Jaime** on Wednesday, February 1, 2012 at 4:01pm.

So far I found the probability distribution of X, where X is the sum of the dice:

2: P(X=x)= .0278

3: P(X=x)= .0556

4: P(X=x)= .0833

5: P(X=x)= .1111

6: P(X=x)= .1389

7: P(X=x)= .1667

8: P(X=x)= .1389

9: P(X=x)= .1111

10: P(X=x)= .0833

11: P(X=x)= .0556

12: P(X=x)= .0278

I also found the expected value of X: 7.

So from this I know that probability of each sum differs, with rolling a sum of 7 being more probable than rolling a sum of 2 or 12.

I'm having some trouble figuring out the expected value of the game, however. Say that to play my game, a person has to pay $1. If he wins, he wins $6, making the net outcome of a win $5. So the two outcomes are: -1 and 5. The way we found the expected value in class was we found the outcomes and the probability of each outcome, multiplied the outcome by the probability, and summed the products. The part that is confusing me is, doesn't the probability of winning depend on the sum that a player guesses? Isn't someone who guesses 7 as their sum going to be more likely to win than someone who guesses a 2?

Am I overthinking this or going about this in the wrong way? Can someone help me figure this out?

**Related Questions**

math - Dice is a popular game in gambling casinos. Two dice are tossed, and ...

Mathematics for Liberal Arts - You are on a TV show. You have been asked to ...

ALGEBRA - Dice is a popular game in gambling casinos. Two dice are tossed, and ...

ALGEBRA - Dice is a popular game in gambling casinos. Two dice are tossed, and ...

Math- Alg 2 - Help finding probability involving combinations? What is the ...

Statistics - The game of chuck-a-luck consists of rolling 3 dice. The player ...

Probability and statistics - A dice game involves rolling 2 dice. If you roll ...

Statistics - In a game you roll two fair dice. If the sum of the two numbers ...

statistics - A gambling game pays 4 to 1 and the chance of winning is 1 in 6. ...

math-i have another question - Player A and B invented a new game. The ...