Respuesta :
Answer:
a) p=0.026
b) q=0.974
c) The casino has a long-run expected profit of $0.43 per bet.
Step-by-step explanation:
a) We have a roulette with 38 slots (37 numbers from 0 to 36, plus the double-0). Then, the probablity of winning if you pick on number (in this case, 7 for instance), can be calculated as the quotient between 1 and 38:
[tex]p=1/38=0.026[/tex]
b) The odds against winning, in the case of only picking one slot, is 37 out of 38. Is the complement of the pobability calculated in point a.
[tex]q=37/38=0.974[/tex]
c) In this case, we have to calculate the expected value of a game where if our number comes up, we get $20, and if it is not, we lose $1.
This can be calculated as the sum of the outcomes multiplied by its probabilties:
[tex]E(X)=p_1X_1+p_2X_2=(1/37)\cdot 20+(37/38)\cdot (-1)=0.54-0.97\\\\E(X)=-0.43[/tex]
With this result, we can conclude that the casino has a long-run expected profit of $0.43 per bet.
