Roulette is a casino game that involves players betting on where a ball will land on a spinning wheel. An American roulette wheel has 38 numbered slots — half of the slots from 1 to 36 are red and the other half are black. Slots 00 and 00 are both green. Suppose that a player bets $1 on a single slot. If the ball lands in their slot, the player gets their initial $1 back plus a payout of $35. If the ball doesn't land in their slot, they lose their $1 bet. Let X= the player's net gain from a $1 bet on a single slot. Here is the probability distribution of X: Find the expected value of a player's net gain on a $1 bet on a single slot. You may round your answer to the nearest thousandth

There is a game of chance called "Lightning Dice" at a charity carnival.  It costs $2 to play.  The player then rolls 4 dice.  If the player rolls 3 or more sixes, then the player wins $30.  Otherwise, the player wins nothing.  How much can you expect to gain or lose if you play this game 68 times?

A friend proposes a gamble to you. You roll 2 fair, six-sided dice, and add up the results of each die to find your total number. If your roll totals a 6 or 8, your friend pays you $30. If you roll any other total, you pay your friend $10. What is your expected payoff from playing this game 100 times?.

a pair of dice is rolled once. Suppose that you lose 9$ if the dice sum to 5 and win 10$ if the dice sum to 11 or 8. How much should you win or lose if any other number turns up in order for the game to be fair?

James placed a $25 bet on a red and a $5 bet on the number 33 (which is black) on a standard 00 roulette wheel.   -if the ball lands in a red space, he wins $25 on his 'red' but loses $5  on his '33' bet - so he wins $20 -if the ball lands the number 33, he loses $25 on his 'red' bet but wins $175 on his '33' bet: He wins $150 -if the ball lands on a spae that isn't red and isnt 33 he loses both bets, so he loses $30 So for each spin; he either wins $150, wins $20, or loses $30 -probability that he wins $150 is 1/38 or .0263 -probability that he wins $20 is 18/38 or .4737 -probability that he loses $30 is 19/38 or .5000   let X = the profit that james makes on the next spin x P (X=x) x*P(X=x) x^2*P(X=x) 150 .0263 3.945 591.75 20 .4737 9.474 189.48 -30 .5000 -15.000 450.00 sum (sigma) 1.000 -1.581 1231.23   u (expected value)= -$1.581 variance = 1228.73044 standard deviation = 35.053   FILL IN THE BLANK   if you play 2500 times, and Let, x (x bar)= the mean winnings (or…

One option in a roulette game is to bet $7 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $7 you paid to play the game and you are awarded $7. If the ball lands elsewhere, you are awarded nothing and the $7 that you bet is collected. Complete parts (a) through (b) below. III a. What is the expected value for playing roulette if you bet $7 on red? $ (Round to the nearest cent.) b. What does this expected value mean? Choose the correct statement below. O A. This value represents the expected loss over the long run for each game played. OB. Over the long run, the player can exper to break even. OC. This value represents the expected win over the long run for each game played.

A certain game involves tossing 3 fair coins, and it pays 11¢ for 3 heads, 7¢ for 2 heads, and 4e for 1 head. Is 7¢a fair price to pay to play this game? That is, does the 7¢ cost to play make the game fair? .... The 7¢ cost to play a fair price to pay because the expected winnings are (Type an integer or a fraction. Simplify your answer.)