Please can you help me (Probability)
posted by Fakaapo. Suetusi .
Maria is playing a game of chance at the Hibiscus festival, costing $1 for each game. In the game two fair dice are rolled and the sum of the numbers that turn up is found. If the sum is seven, then Maria wins $5. Otherwise Maria loses her money.
a) Please can you Construct Maria’s probability distribution for gaining.
Thank you for your help.

There are 36 possible outcomes which can be grouped into 11 events E represented by the totals of 2 to 12, each with probability P(E).
For example construct the probability distribution table:
E P(E)
2 1/36 (only one way to make a sum of 2)
3 2/36 (two ways to make a sum of 3)
4 3/36 (3 ways to make 4: 1+3,2+2,3+1)
...
12 1/36
The gain for each event is G(E)= 1 except for E=7 where the gain is G(7)=5.
The expected gain is ∑G(E)P(E) for all E.