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When playing roulette at a​ casino, a gambler is trying to decide whether to bet ​$15 on the number 34 or to bet ​$15 that the outcome is any one of the five possibilities 00 comma 0 comma 1 comma 2 comma or 3. The gambler knows that the expected value of the ​$15 bet for a single number is negative 0.79 cents. For the ​$15 bet that the outcome is 00 comma 0 comma 1 comma 2 comma or 3​, there is a probability of StartFraction 5 Over 38 EndFraction of making a net profit of ​$75 and a StartFraction 33 Over 38 EndFraction probability of losing ​$15. a. Find the expected value for the ​$15 bet that the outcome is 00 comma 0 comma 1 comma 2 comma or 3. b. Which bet is​ better: a ​$15 bet on the number 34 or a ​$15 bet that the outcome is any one of the numbers 00 comma 0 comma 1 comma 2 comma or 3​? ​Why?

Respuesta :

Answer:

A) -$3.16; B) A $15 on the number 34

Step-by-step explanation:

To find the expected value, we multiply the probability of winning by the amount won, multiply the probability of losing by the amount lost, and add the two.

The probability of winning is 5/38 and the net profit will be $75:

5/38(75) = 375/38 ≈ $9.87

The probability of losing is 33/38 and the amount lost will be $15:

33/38(-15) = -495/38 ≈ -$13.03

We now add these amounts:

9.87+-13.03 = -3.16

Since the expected value on a single number is -$0.79 and the expected value on any one of the given numbers in the set is -$3.16, the safer bet would be on the number 34.

a) The expected value of the $15 bet is of -$3.16.

b) The bet on a single number is better, as it has a higher expected value.

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Item a:

  • 5/38 probability of earning $75.
  • 33/38 probability of losing $15.

The expected value is the sum of each outcome multiplied by it's respective probability, thus:

[tex]E(X) = 75\frac{5}{38} - 15\frac{33}{38} = \frac{75(5) - 15(33)}{38} = -3.16[/tex]

The expected value of the $15 bet is of -$3.16.

Item b:

  • The expected value of the bet on a single number is of -$0.79.
  • It is higher than the expected value of the bet on multiple numbers, so the best bet is a bet on a single number.

A similar problem is given at https://brainly.com/question/24855677

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