Question

Fernando is trying to decide which of 2 roulette games to play at a casino, where each

roulette has 30 slots. Each game, Fernando wants to bet on a single slot. In the first
roulette game Fernando has to invest $5 to play, if he wins he gets his investment back
plus $1000, if he loses, he loses his investment. In the second roulette game, he invest
$1 to play, if he wins he gets his investment back plus $200 and if he loses, he loses his
investment. Calculate the expected value of the net gain for each roulette game and assume
that Fernando will go with the game that gives him the higher value.

Answer 1

Fernando should choose the first roulette game as it has a higher expected value of $28.50, compared to the second game's $5.70 expected value, when considering the probability and payout of each game.

Step-by-step explanation:

Fernando is trying to decide which of two roulette games to play based on their expected values. To calculate this, we consider the net gains for each outcome and the probability of each outcome occurring. For the first roulette game, the probability of winning is 1/30 and the probability of losing is 29/30. The expected value (EV) for this game is calculated as follows: EV = (1/30) * ($1000) + (29/30) * (-$5).

For the second roulette game, the probability of winning and losing remains the same, but the amounts change. So, the expected value for the second game is: EV = (1/30) * ($200) + (29/30) * (-$1).

Fernando would choose the game with the higher EV. To complete the calculations, for the first game: EV = (1/30) * $1000 - (29/30) * $5 = $33.33 - $4.83 = $28.50. For the second game: EV = (1/30) * $200 - (29/30) * $1 = $6.67 - $0.97 = $5.70. Thus, Fernando should choose the first game with the higher expected value of $28.50.