Question

One plays a game where you spin a spinner with the numbers 1 through 10 on it in equal parts.  It costs $7 to play.  If you spin a two then you win $25.  If you spin an odd number then you win $10.  You decide to play the game once.  What are your expected winnings?

Answer 1

Consider the following table:

Number	Probability	Expected Payout	Expected Payout - 7
1	0.1	10	3
2	0.1	25	18
3	0.1	10	3
4	0.1	0	-7
5	0.1	10	3
6	0.1	0	-7
7	0.1	10	3
8	0.1	0	-7
9	0.1	10	3
10	0.1	0	-7

The expected winnings can be calculated as:

(Expected Payout - 7) * Probability

Number	Probability	Expected Payout	Expected Payout - 7	(Expected Payout - 7) * Probability
1	0.1	10	3	0.3
2	0.1	25	18	1.8
3	0.1	10	3	0.3
4	0.1	0	-7	-0.7
5	0.1	10	3	0.3
6	0.1	0	-7	-0.7
7	0.1	10	3	0.3
8	0.1	0	-7	-0.7
9	0.1	10	3	0.3
10	0.1	0	-7	-0.7
				0.5

Your expected winnings are $0.5

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