ByMario303
In a game of chance, a standard dice is used. A game costs 1 euro. If a 6 is rolled, you receive 3 euros. If a 2 or 4 is rolled, you still receive 1.50 euros.
a) How would the stake have to be changed so that the player statistically makes a profit of 8 euros when playing 10 times?
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For 10 times a win of 8,- € per game means a win of 0.8 €.
That is. You must now set the expected value equal to 0.8 with unknown use.
And the expected value with respect to the profit is, as is known, the sum of “Truthfulness mal Profit” of all “Gewinnstaffeln”, i.e. here: E=1/6 * (3-x) + 2/6 * (1,5-x) – 3/6 * x.
That is. You have to dissolve this for E=0.8 after x (x=use per game).