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lyudmila [28]
3 years ago
13

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 t

o 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?
Mathematics
1 answer:
cricket20 [7]3 years ago
6 0

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)                \dfrac{33}{38}                        \dfrac{5}{38}

a)  The expected value of X is given by:

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

=-0.39

= -39 \ cents

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

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