Question

A roulette wheel has 38 slots, numbered 0 through 36, with the remaining slot numbered 00. A is released, into the spinning roulette wheel and ends up in a random slot, with equal likelihood each slot, when the wheel spins down. A player wins $1 if the slot in which the ball ends up is numbe.

19:36 and wins nothing otherwise. What is the expected value of the Player's winnings?
Round to 4 decimal places if needed.

Answer 1

The expected value of the player's winnings in roulette is $0.4737 per spin, calculated by multiplying the payout of each outcome by their respective probabilities and summing these products.

Step-by-step explanation:

To calculate the expected value of the player's winnings in roulette, we use the formula for expected value:
E(X) = ∑ [xi × P(xi)], where xi is the value of each outcome and P(xi) is the probability of that outcome occurring.

There are 38 possible outcomes on a roulette wheel (numbers 0, 00, and 1 through 36). A player wins $1 if the ball lands on numbers 19 through 36, which is a total of 18 numbers. The probability of winning is P(win) = 18/38.

The probability of winning nothing is P(lose) = 20/38, since there are 20 other numbers (0, 00, and numbers 1-18) that will not result in a win.

Using this information, we calculate the expected value as follows:
E(X) = ($1 × 18/38) + ($0 × 20/38) = $0.4737 (rounded to four decimal places).

Therefore, the expected value of the player's winnings is $0.4737 per spin.