An American roulette wheel has 38 slots, of which 18 are black, 18 are red, and 2 are green. When the wheel is spun, the ball is equally likely to come to rest in any of the slots. Gamblers bet on the roulette by placing chips on a table that lays out the numbers and colors of the 38 slots in the roulette wheel. The red and black slots are arranged on the table in three columns of 12 slots each. A $1 column bet wins $3 if the ball lands in one of the 12 slots in that column.
The expected amount you win in a column bet is $ ?
The expected amount you win in a column bet is $1.
To find the expected amount you win in a column bet, we need to calculate the probability of winning and losing, as well as the respective payouts.
In this case, we have three columns of 12 slots each, making a total of 36 slots (12 in each column). The probability of winning a column bet is the number of favorable outcomes (the ball landing in one of the 12 slots in that column) divided by the total number of possible outcomes (the 38 slots on the roulette wheel).
So, the probability of winning a column bet is 12/38, as there are 12 favorable outcomes (slots in the chosen column) out of 38 possible outcomes (total number of slots on the wheel).
Now, let's consider the payout for a column bet. It states that a $1 column bet wins $3 if the ball lands in one of the 12 slots in that column.
Therefore, the expected amount you win in a column bet can be calculated as follows:
Expected Amount = (Probability of winning) * (Payout for winning) + (Probability of losing) * (Payout for losing)
In this case, the probability of winning is 12/38, and the payout for winning is $3. Since the column bet is a win-or-lose bet, the probability of losing is 1 - (12/38) = 26/38, and the payout for losing is $0.
Thus, the expected amount you win in a column bet can be calculated as:
Expected Amount = (12/38) * $3 + (26/38) * $0 = $0.7908 (rounded to four decimal places)
Therefore, the expected amount you win in a column bet is approximately $0.7908.
To calculate the expected amount you win in a column bet, we need to find the probability of the ball landing in one of the 12 slots in that column.
Out of the 38 slots on the roulette wheel, there are 12 slots in the column you bet on. So, the probability of winning the bet is 12/38.
If you win the bet, you receive $3 for every $1 you bet. Therefore, the win amount is $3.
To calculate the expected amount, we multiply the probability of winning by the win amount:
Expected win amount = probability of winning x win amount
Expected win amount = (12/38) x $3
Simplifying this calculation, we have:
Expected win amount = $0.1579 x $3
Expected win amount = $0.4737
The expected amount you win in a column bet is approximately $0.47.