The game is profitable since the payout is always less than what you earn.
Given that a fair game with 4 or more outcomes using a binomial situation presented in this lesson (simulated with a spinner or random number) and adjust the point values the so cost of the 10 points will make the game profitable.
Let's discuss the Lucky 7 game
The game is played with the two fair dice rolls.
You put your money on either of 3 things: Above 7, Lucky 7 or below 7
The game below is designed in Excel:
Each cell formula to generate the game:
They are 36 possible outcomes.
7 is the most likely number coming up
6/36=1/6
of the time.
Thus the expected value of the bet is:
(5/12)x₂+(5/12)x₂+(1/6)x₃=26/12
Which, of course, can not make any sense. so, the good idea from the standpoint of the bank is to pay two times on only one of the two possibilities, not a seven, and to give the bet back on the 7. This then gives:
(5/12)x₂+(5/12)x₀+(1/6)x₁=12/12=1
Which is a perfectly fair game.
Of course, the bank wouldn't approve either, so we probably need more restrictions. The way 7 comes out is: 2 ways for each case, (1,5), (2,5), (3,4), then a constraint like not to pay on (5,1) would be added.
Then the 7 returns the money
4/36 = 1/9.
The new case then yields:
(5/12)x₂+(5/12)x₀+(1/9)x₁=34/36=17/18
This says that for every $18 handled in bets the bank expects to pay out $17.
Hence we can say that the game is profitable since the payout is always less than what you earn.
Learn more about fair game from here brainly.com/question/7669874
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