A roulette wheel has the numbers 1 through 36, 0, and 00. A bet on four numbers pays 8 to 1 (that is, if you bet $1 and one of the four numb

Question

A roulette wheel has the numbers 1 through 36, 0, and 00. A bet on four numbers pays 8 to 1 (that is, if you bet $1 and one of the four numbers you bet comes up, you get back your $1 plus another $8). How much do you expect to win with a $1 bet on four numbers? HINT [See Example 4.] (Round your answer to the nearest cent.)

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Claire 2 weeks 2021-09-13T14:06:25+00:00 1 Answer 0

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    2021-09-13T14:08:05+00:00

    Answer:

    Lose $0.05

    Step-by-step explanation:

    There are 38 possible spots on the roulette wheel (numbers 1 to 36, 0 and 00).

    If the player can choose four numbers on single $1 bet, his chances of winning (W) and losing (L) are as follows:

    P(W) = \frac{4}{38} \\P(L) = 1-P(W) = 1-\frac{4}{38} \\P(L) = \frac{34}{38}

    The expected value of the bet is given by the probability of winning multiplied by the payout ($8), minus the probability of losing multiplied by the bet cost ($1)

    EV=\frac{4}{38}*\$8 -\frac{34}{38}*\$1\\EV= -\$0.05

    On each bet, the player is expected to lose 5 cents ($0.05).

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