In the game of roulette a player can place a 8 bet on the...

In the game of roulette, a player can place a $8 bet on the number 22 and have a 138 probability of winning. If the metal ball lands on 22, the player gets to keep the $8 paid to play the game and the player is awarded an additional $280. Otherwise, the player is awarded nothing and the casino takes the player's $8. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:01 All right, and your question, you're playing the game of roulette, and a player is betting $8, and they're going to play the number 22.

00:14 So bet $8 on $22, and you're being told that the probability of a 22 coming up is 1 out of 38.

00:26 And we're told the odds, you end up getting to, you win $280, if it lands on 22.

00:39 Yes, you get to keep the $8, but your net gain, like what you actually gained, would have been $280.

00:46 If you lose the game, you lose $8.

00:51 So what you're being asked to calculate, you're asked to do two problems here.

00:56 The first question is, what's the expected value? so usually we put the expected value as e of x.

01:04 That's usually the symbol for expected value.

01:06 And we want to take each possible outcome.

01:10 So we have two outcomes here.

01:12 We could win and we could lose, which would be a negative 8.

01:18 We want to multiply them those outcomes to the probabilities of those outcomes.

01:24 So this is 1 out of 38.

01:26 This is 37 out of 38.

01:29 We have 37 out of 38 chance of losing.

01:32 Once we multiply each outcome to the probability of that outcome, we add each of those.

01:38 So now we're just going to go ahead and type that in the calculator...

Question

Please give Ace some feedback