Please can you help me (Probability)

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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.

• Please can you help me (Probability) -

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.

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