expected value problem (statistics)

Question

if a player rolls 2 dice and gets a sum of 2 or 12, he wins $20. if the person gets a 7, he wins $5. the cost to play is $1.

a) Make a probability for this situation

b) calculate the expected value

c) what does the expected value mean in the context of this situation?

Answer 1

Use a table (which is hard to make in this tool). On the left column, list the sum of each roll. In the second column, list the net gain/cost of the roll. In the third column, list the probability of each roll. Then multiply column 2 times column 3 and add them all up. The first few rows of the table should look like this

Sum | Gain/Loss | Probability

========================

2 | 19 | 1/36

3 | -1 | 2/36

4 | -1 | 3/36

....

If you roll a 2, you paid $1 and get $20, so your net is $19.

There are two ways to roll a 3: 12, 21.

There are three ways to roll a 4: 13, 22, 31.

...and so on.

Can you take it from there?