Question

Fernando is trying to decide which of

2 roulette games to play at a casino, where each roulette has 38 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

The first roulette game has a higher expected value of $21.45 compared to $4.29 for the second game, so Fernando should choose to play the first game for higher expected net gains.

Step-by-step explanation:

The question is asking us to calculate the expected value of the net gain for each of the two roulette games Fernando is considering playing. Since each roulette has 38 slots and Fernando is betting on a single slot, the probability of winning on any given play is 1/38 and the probability of losing is 37/38. To calculate the expected value for each game, we can use the formula:

Expected Value (EV) = (Probability of Winning x Amount Won) - (Probability of Losing x Amount Lost).

First Roulette Game:

Investment: $5
Win: $1000
Probability of Winning: 1/38
Probability of Losing: 37/38
EV = (1/38 x $1000) - (37/38 x $5)
EV = $26.32 - $4.87
EV = $21.45

Second Roulette Game:

Investment: $1
Win: $200
Probability of Winning: 1/38
Probability of Losing: 37/38
EV = (1/38 x $200) - (37/38 x $1)
EV = $5.26 - $0.97
EV = $4.29

Based on these calculations, the first roulette game has a higher expected net gain of $21.45 compared to $4.29 for the second game. Therefore, Fernando should choose the first game.