Final answer:
The student's question involves calculating the expected value for a roulette bet, considering the probabilities of winning or losing. The expected value indicates an average loss per game over time, meaning that the house has the advantage in this scenario.
Step-by-step explanation:
The question involves the concept of probability and expected value, commonly studied in mathematics, particularly in high school or introductory college courses focused on statistics or probability.
Expected value is a concept in probability that represents the average outcome you would expect over many repetitions of a particular random event. To calculate the expected value when betting on a roulette wheel, as in the example given, you multiply each possible outcome by its associated probability and sum these products together.
Given that there's a 20/38 chance of losing (approximately 0.5263), and assuming an 18/38 chance of winning since the question doesn’t specify otherwise, the expected value is computed as: (18/38) * $1 + (20/38) * (-$1) which gives a negative expected value indicating an average loss per game over time.
The example provided with the odds of 252 to 45 indicates a situation where on average, you would break even and thus not yield a profit, meaning it is not a good betting strategy. Similarly, if the expected value is negative, as in the roulette scenario, the house has the advantage, and over time, the player will lose money.