Question

One of the wagers in the game of roulette is to place a bet that the ball will land on a red number. (Eighteen of the numbers are black, 18 are red, and two are green.) If the ball lands on a red number, the player wins the amount of his bet. If a player bets $5, find the player's expectation.

Answer 1

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 $S_1 = 5$

$P(S_1) = \frac{18}{38}$

For $S_2 = -5$(negative sign represents the loss)

$P(S_2) = \frac{20}{38}$

Now, use the above formula.

$E(x) = 5\times \frac{18}{38}-5\times \frac{20}{38}$

$E(x) = \frac{90}{38}-\frac{100}{38}$

$E(x) = \frac{-10}{38}$

$E(x) = -0.2632$

Hence, the expectation is -$0.2632