What is the expectation for the $1 bets on a U.S. roulette wheel? See the figure. (Round your answer to the nearest cent.)
Three-number bet
Thank you
Using the figure, It say this type of bet pays 11 to 1. So the answer equals $11(3/38)+($-1)(35/38)-$0= -0.0526. Which rounds to -0.05.
what about a six number bet?
Well, my gambling friend, let's take a spin on this question! When you place a $1 three-number bet on a U.S. roulette wheel, the expectation can be calculated. Now, I don't have a crystal ball, but I do have some math skills!
On a U.S. roulette wheel, there are 38 possible outcomes since there are 18 red numbers, 18 black numbers, and 2 green numbers (0 and 00). So, the probability of winning a three-number bet is 3/38.
If you win a three-number bet, you get a payout of 11 to 1. That means, if you bet $1 and win, you'll get $11 back.
To calculate the expectation, you multiply the probability of winning by the winnings and subtract the probability of losing multiplied by the bet amount.
Expectation = (Probability of winning × Winnings) - (Probability of losing × Bet)
Expectation = ((3/38) × $11) - ((35/38) × $1)
Now, let's do the math:
Expectation = ($0.2895) - ($0.9211)
After rounding to the nearest cent, the expectation for a $1 three-number bet on a U.S. roulette wheel is approximately -$0.63.
So, my friend, based on these calculations, you should expect to lose around 63 cents on each $1 three-number bet you make. Remember, though, in the world of gambling, anything can happen!
To calculate the expectation for a $1 bet on a three-number bet in a U.S. roulette wheel, we need to consider the probability of winning and losing, as well as the amount won or lost.
In a three-number bet, you are betting on three consecutive numbers on the roulette wheel. There are a total of 38 numbers on a U.S. roulette wheel, including the numbers 1 through 36, 0, and 00.
The probability of winning a three-number bet is 3/38, since there are three possible winning numbers out of the 38 total numbers on the wheel.
If you win, the payout for a three-number bet is typically 11 to 1. This means if you bet $1 and win, you will receive $11 in winnings plus your original $1 bet back.
On the other hand, if you lose, you will lose your entire $1 bet.
To calculate the expectation, we can multiply the probability of winning by the amount won, and subtract the probability of losing multiplied by the amount lost.
Expectation = (probability of winning * amount won) - (probability of losing * amount lost)
Expectation = (3/38 * $11) - (35/38 * $1)
Calculating this, we get:
Expectation ≈ $0.2895 - $0.9211
Expectation ≈ -$0.6316
Rounding this to the nearest cent, the expectation for a $1 bet on a three-number bet in a U.S. roulette wheel is approximately -$0.63.
To calculate the expectation for the $1 bets on a U.S. roulette wheel, we need to determine the probability of winning and the amount won or lost.
In the case of a three-number bet, also known as a "street" bet, you place a $1 bet on three adjacent numbers on the roulette table. There are 38 numbers on a U.S. roulette wheel, including 0 and 00. For a three-number bet, there are 3 ways to win and 35 ways to lose.
To determine the probability of winning, we divide the number of winning outcomes by the total number of possible outcomes:
Probability of winning = 3 / 38
To calculate the amount won or lost, we consider that if you win, the casino pays out at a rate of 11 to 1. This means that if you win, you get your original $1 bet back plus $11 in winnings. If you lose, you lose your $1 bet.
Now, we can calculate the expectation by multiplying the probability of winning by the amount won or lost:
Expectation = (Probability of winning * Amount won) - (Probability of losing * Amount lost)
= ((3 / 38) * ($11)) - ((35 / 38) * ($1))
To get the answer, we can plug in the values and use a calculator to round the result to the nearest cent.