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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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Which equation could have the graph shown below? y = (x – 4)(x – 1)(2 + x)(3 + x) y = (x – 4)(1 – x)(2 + x)(3 + x) y = (x + 4)(x
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If you were to graph this, you would see that the function's line interesects the x-axis at these points... when x=4, when x=1, etc etc.

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. Among all the income tax forms filed in a certain year, the mean tax paid was $2000, and the standard deviation was $500. In a
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Answer:

a) 0.8413

b) 0.6293

Step-by-step explanation:

Data provided:

Mean tax paid = $2000

Standard deviation = $500

Sample size, n = 625

n=625

Now,

a) P( average tax paid on the sample forms is greater than $1980)

⇒ P(X > 1980)

or

⇒ P(\frac{(X-mean)}{\frac{s}{\sqrt n}})

or

⇒ P(\frac{(1980-2000)}{\frac{500}{\sqrt{625}}})

or

⇒ P(Z > -1)

or

= 0.8413 (From standard normal table)

b) P(more than 60 of the sampled forms have a tax of greater than $3000)

given:  p = 10% = 0.1

Now, by using CLT

mean = n × p

= 625 × 0.1

= 62.5

Standard deviation, s =\sqrt{n\times p\times(1-p)}

=\sqrt{625\times0.1\times(1-0.1)}

= 7.5

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= P(\frac{(X-mean)}{s} > \frac{(60-62.5)}{7.5})

or

= P(Z > -0.33)

= 0.6293     (From standard normal table)

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