Question

When playing roulette at a casino, a gambler is trying to decide whether to bet $15 on the number 30 or to bet $15 that the outcome is any one of the three possibilities 00, 0, or 1. The gambler knows that the expected value of the $15 bet for a single number is $1.58. For the $15 bet that the outcome is 00, 0, or 1, there is a probability of 3/38 of making a net profit of $45 and a 35/38 probabiity of losing $15. Find the expected value for the $15 bet that the outcome is 00, 0, or 1

Answer 1

The expected value for the $15 bet that the outcome will be 00, 0, or 1 in a roulette game is calculated as -$10.26, implying an average loss of $10.26 per game.

Step-by-step explanation:

The question asks to find the expected value of a $15 bet in roulette when betting on the outcomes 00, 0, or 1. To calculate this, we use the information provided to determine the potential profit and the probabilities associated with winning and losing the bet. The expected value (EV) formula is:

EV = (Net Profit × Probability of Winning) + (Net Loss × Probability of Losing)

According to the given scenario, there are two outcomes: winning a net profit of $45 with a probability of 3/38, and losing the bet amount of $15 with a probability of 35/38. Using the formula, we get:

EV = ($45 × 3/38) + (-$15 × 35/38)

EV = ($135/38) + (-$525/38)

EV = -$390/38

EV = -$10.26

Therefore, the expected value for the $15 bet on outcomes 00, 0, or 1 in roulette is -$10.26, which means on average, the gambler will lose $10.26 per game.