Question

A roulette wheel has the numbers 1 through 36, 0, and 00. A bet on five numbers pays 6 to 1 (that is, if one of the five numbers you bet comes up, you get back your $1 plus another $6). How much do you expect to win with a $1 bet on five numbers? HINT [See Example 4.] (Round your answer to the nearest cent.)

Answer 1

Answer:

5 cents

Step-by-step explanation:

So the roulette wheel would have a total of 38 numbers, which means 38 different possible cases. Since you are allowed to bet on 5 numbers, the chance to win this is 5 out of 38 and to lose this is 33 out of 38.

If you win, you get 1 + 6 = 7 dollar, and if you lose, you lose 1 dollar.

Therefore the expected amount out of this game is:

$E = 7\frac{5}{38} - 1\frac{33}{38} = \frac{35}{38} - \frac{33}{38} = \frac{2}{38} = \frac{1}{19} = \ 0.0526$

or 5 cents