The expected value of betting 32 is -$0.053, making the 4th option the right choice.
In the question, we are asked for the expected value of betting on 32, given that if we bet $1 on the number 32 and win, the house pays $36, and there are 38 slots.
The probability distribution can be shown as:
x $35 -$1
p(x) 1/38 37/38
as, if we get 32, which has the probability of 1/38, the winning number, we gain $35, and for the rest, having a probability of 37/38, the losing number, we lose -$1.
Thus, the expected value can be calculated as E(x) = ∑x.p(x).
Thus, the expected value = $35(1/38) + (-$1)(37/38) = -$2/38 = -$0.05263 ≈ -40.053.
Hence, the expected value of betting 32 is -$0.053, making the 4th option the right choice.
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