Respuesta :
Answer:
[tex] E(X) = 11 *\frac{4}{52} - 1*\frac{48}{52} = -\frac{1}{13}[/tex]
So we expect to lose approximately [tex] 1/13[/tex] for this game.
Step-by-step explanation:
For this case we can find the probability of win like this:
[tex] p_w = \frac{4}{52}[/tex]
Since we have 4 aces each time in a total of 52.
And the probability of loss is given by:
[tex] p_l = \frac{48}{52}[/tex]
In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".
And we can find the expected value with this formula:
[tex] E(X) = \sum_{i=1}^n X_i P(X_i) [/tex]
Where X on this case represent the random variable "Amount of money win or loss in the game", for this case we can replace and we got:
[tex] E(X) = 11 *\frac{4}{52} - 1*\frac{48}{52} = -\frac{1}{13}[/tex]
So we expect to lose approximately [tex] 1/13[/tex] for this game.
