In how many ways can we choose one number from the set $\{1,2,3\}$, one number from the set $\{4,5,6\}$, and one number from the
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<h3>Answer: 4</h3>
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Explanation:
Refer to the table below (attached image). I've copied your table and added a third row at the bottom. This new row is the result of multiplying each payout value with the corresponding probability.
Example: for the first entry of this row, have 2*0.45 = 0.9
Once that third row is filled out, you add up everything in that row. That will lead to the expected value.
The expected value is: 0.9+1.2+0.6+0.8+0.5 = 4
Interpretation: You expect, on average, to win $4 each time you play the game. This assumes that the cost to play the game is 0 dollars. If the cost is something else, then it will affect the expected value.
Because the expected value is not 0, this game is not mathematically fair (the bias is leaning in favor of the player).