How Do You Calculate Expected Value in a Dice Game?

[AnnBean]

I really need help on how to solve this (Sweating):

A dice game involves rolling 2 dice. If you roll a 2, 3 , 4, 10, 11 or a 12, you win \$5. If you roll a 5, 6, 7, 8, or 9, you lose \$5. Find the expected value you win (or lose) per game.

 

[MarkFL]

Re: Probability

Hello, and welcome to MHB, AnnBean! (Wave)

I would begin by constructing a table as follows:

Sum $S$	Probability of $S$: $P(S)$	Net Gain/Loss (in dollars) $G$	Product $G\cdot P(S)$
2	$\dfrac{1}{36}$	5	$\dfrac{5}{36}$
3	$\dfrac{1}{18}$	5	$\dfrac{5}{18}$

Can you complete the table?

 

[MarkFL]

Re: Probability

Just to follow up, here is the completed table:

Sum $S$	Probability of $S$: $P(S)$	Net Gain/Loss (in dollars) $G$	Product $G\cdot P(S)$
2	$\dfrac{1}{36}$	5	$\dfrac{5}{36}$
3	$\dfrac{1}{18}$	5	$\dfrac{5}{18}$
4	$\dfrac{1}{12}$	5	$\dfrac{5}{12}$
5	$\dfrac{1}{9}$	-5	$-\dfrac{5}{9}$
6	$\dfrac{5}{36}$	-5	$-\dfrac{25}{36}$
7	$\dfrac{1}{6}$	-5	$-\dfrac{5}{6}$
8	$\dfrac{5}{36}$	-5	$-\dfrac{25}{36}$
9	$\dfrac{1}{9}$	-5	$-\dfrac{5}{9}$
10	$\dfrac{1}{12}$	5	$\dfrac{5}{12}$
11	$\dfrac{1}{18}$	5	$\dfrac{5}{18}$
12	$\dfrac{1}{36}$	5	$\dfrac{5}{36}$

Summing up the $G\cdot P(S)$, column, we find the expected value is:

\(\displaystyle \text{EP}=-\frac{5}{3}\)