Question

one of the wagers in roulette is to bet that the ball will stop on a number that is a multiple of 3. (both 0 and 00 are not included.) if the ball stops on such a number, the player wins double the amount bet.
suppose a player bets $1.
find the probability that the ball stops on a number that is a multiple of 3. (enter your probability as a fraction.)
6/19
how much money (in dollars) will the player win if the ball stops on a multiple of 3?
$ 1
find the probability that the ball does not stop on a number that is a multiple of 3. (enter your probability as a fraction.)
13/19
how much money (in dollars) will the player lose if the ball does not stop on a multiple of 3?
$ 1
compute the players expectation (in dollars). (round your answer to two decimal places.)
$ 0.37
enter a number.
show my work (optional)

Explanation:

Step1: Calculate the expected value formula

The formula for expected value \(E(X)\) is \(E(X)=\sum_{i}x_ip_i\), where \(x_i\) are the outcomes and \(p_i\) are their respective probabilities. Here, when the ball stops on a multiple of \(3\) (\(x_1 = 1\), \(p_1=\frac{6}{19}\)), and when it doesn't (\(x_2=- 1\), \(p_2=\frac{13}{19}\)).

Step2: Substitute values into the formula

$$
LATEXBLOCK0
$$

Answer:

\(-0.37\)