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andy6128
02.06.2020 •
Mathematics
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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Ответ:
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{5}{38}](/tpl/images/0674/1458/efc35.png)
a) The expected value of X is given by:
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
Ответ:
A. (
)² =
×
= ![\frac{1}{4}](/tpl/images/0525/0275/0d86b.png)
Step-by-step explanation:
Answer choice (A) is the counterexample because squaring number
results into number
which is less than
.