When playing roulette at the Venetian casino in Las Vegas, a gambler is trying to decide whether to bet $5 on the number 27 or to bet $5 that the outcome is any one of these five possibilities: 0, 00, 1, 2, 3. From Example 6, we know that the expected value of the $5 bet for a single number is -26. For the $5 bet that the outcome is 0, 00, 1, 2, or 3, there is a probability of 5>38 of making a net profit of $30 and a 33>38 probability of losing $5.
a. Find the expected value for the $5 bet that the outcome is 00, 0, or 1.
b. Which bet is better: a $5 bet on the number 25 or a $5 bet hat the outcome is any one of the numbers 00, 0, or 1? Why?

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2020-06-03T04:23:54+02:00

Answer:

Step-by-step explanation:

Given that:

To bet $5 that the outcome is any one of these five possibilities: 0, 00, 1, 2, 3.

Let Y represent the Amount of net profit

Then, Y= {-5, 30}

The probability distribution of Y is:

Y -5 30

P(Y=y) [tex]\dfrac{33}{38}[/tex] [tex]\dfrac{5}{38}[/tex]

a) The expected value of X is given by:

[tex]E[Y] =\sum y P(Y=y)= 30*\dfrac{5}{38}-5*\dfrac{33}{38}[/tex]

[tex]=-0.39[/tex]

[tex]= -39 \ cents[/tex]

b)

On a bet of $5 on the number 25 we are expected to loose 24 cents.

While on a $5 bet that the outcome is any one of the numbers 0,00, or 1 we are expected to loose 39 cents.

Hence, $5 bet on the number 27 is better. Because the expected loss is less in this bet