When playing roulette at a casino, a gambler is trying to decide whether to bet $5 on the number 25 or to bet $5 that the outcome is any one of the three possibilities, 00, 0, or 1. The gambler knows that the expected value of the $5 bet for a single number is - 53 cents. For the $5 bet that the outcome is 00, 0, or 1, there is a probability of 3/38 of making a net profit of $20 and a 35/38 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?

Question

Mathematics

Trujillo

30 June, 19:30

When playing roulette at a casino, a gambler is trying to decide whether to bet $5 on the number 25 or to bet $5 that the outcome is any one of the three possibilities, 00, 0, or 1. The gambler knows that the expected value of the $5 bet for a single number is - 53 cents. For the $5 bet that the outcome is 00, 0, or 1, there is a probability of 3/38 of making a net profit of $20 and a 35/38 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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Answers (1)

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Brandon · Answer 1

a) - $3.03; b) The $5 on the number 25

Step-by-step explanation:

To find the expected value, multiply each probability by its value and then add them together.

The probability of making a profit of $20 is 3/38; this gives us

3/38 (20) = 60/38

The probability of losing $5 is 35/38; this gives us

35/38 (-5) = - 175/38

Together, this gives us

60/38-175/38 = - 115/38 ≈ $-3.03

b) Since the expected value for the $5 bet on a single number is $-0.53, and the expected value for the $5 on either 00, 0 or 1 is $-3.03, the better bet is on the number 25. The expected value loses less money with this option.