Respuesta :
Answer:
The expectation is -$0.2632
Step-by-step explanation:
Consider the provided information.
The total number of balls are: 18 red + 18 black + 2 green = 38
If the ball lands on a red number, the player wins the amount of his bet.
The bat is ball will land on a red number.
The favorable outcomes are 18/38 and unfavorable are 20/38.
Let S be possible numerical outcomes of an experiment and P(S) be the probability.
The expectation can be calculated as:
E(x) = sum of S × P(S)
For [tex]S_1 = 5[/tex]
[tex]P(S_1) = \frac{18}{38}[/tex]
For [tex]S_2 = -5[/tex](negative sign represents the loss)
[tex]P(S_2) = \frac{20}{38}[/tex]
Now, use the above formula.
[tex]E(x) = 5\times \frac{18}{38}-5\times \frac{20}{38}[/tex]
[tex]E(x) = \frac{90}{38}-\frac{100}{38}[/tex]
[tex]E(x) = \frac{-10}{38}[/tex]
[tex]E(x) = -0.2632[/tex]
Hence, the expectation is -$0.2632
