13 October, 12:18

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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1. 13 October, 13:28
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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.