Question

In a game of mini roulette, the dealer spins a ball around a wheel with eight slots numbered from 1 to 8. The ball has an equal chance of landing in any of the eight slots. If the dealer pays out $10 for any number between 1 and 6 and $20 for any number between 7 and 8, determine the expected value of a bet on this mini roulette game.

Answer 1

To find the expected value of a bet on mini roulette with uneven payouts across eight slots, we calculate the expected payout for each set of numbers and sum them, resulting in an expected value of $12.50 for the game.

Step-by-step explanation:

To determine the expected value of a bet on mini roulette where there are eight slots and the payouts differ, we need to use the formula for expected value: E(X) = (x1 ∙ p1) + (x2 ∙ p2) + ... + (xn ∙ pn), where x represents the payouts and p the probability of each outcome.

Since the game pays out $10 for slots 1 through 6, and there are 6 such slots, the probability of landing on any one of those slots is 6/8 or 0.75. The game pays $20 for slots 7 and 8, with the probability for each being 1/8 or 0.125.

The expected value is calculated as follows:

• For slots 1-6: $10 ∙ (6/8) = $7.50
• For slots 7-8: $20 ∙ (2/8) = $5.00

Add these two amounts together to obtain the total expected value: $7.50 + $5.00 = $12.50.

Thus, the expected value of a bet on this mini roulette game is $12.50.