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.)

Answer 1

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).