In the casino game of american roulette the wheel is divided...

In the casino game of American roulette, the wheel is divided into 38 compartments numbered 1 through 36, 0, and 00. One-half of the numbers 1 through 36 are red, the other half black, and 0 and 00 are green. Of the many types of bets that may be placed, one type involves betting on the outcome of the color of the winning number. For example, one may place a certain sum of money on red. If the winning number is red, one wins an amount equal to the bet placed and the amount of the bet is returned; otherwise, one loses the amount of the bet. If a player placed a $61 bet on red and a $61 bet on black in a single play in American roulette, what would be the expected value of his winnings? (Round your answer to the nearest cent.)

Transcript

00:01 Hello everyone so this is the question that we have we have in the casino game of american rowley the wheel is divided into 38 compartments of wheel is divided divided into 38 compartments numbered from 1 through 36 0 and double 0 now one half of the numbers 1 through 36 one half from 1 through 36 through 36 are red and the other half are black and the other half are black and zero and double zero are green they are green so now of the many types of the bet may be placed in each american rowler as you may know now, for example, if somebody puts the money on red and if the winning number is red, one wins an amount for the bet placed.

01:18 So if a player bets, so player, player bets, $61 on red and a $61 on black in a single play.

01:43 In a single play so what would be the expected value of his winnings what would be the expected value of his winnings what would be the expected value of his winnings his winnings let's find the answer to this questions so let's find the probability on odds so odds of ball landing on it as they're half way through it there are 38 compartments there are 38 compartments so odds of ball landing on red so out of these 38 zero is gone and double zero are gone for gray how many left 36 so half are red so out of these 36 18 are red and how many total compartments i have 38 so odds of ball landing on red is 18 divided by 38 similarly odds of ball landing on black again 18 divided by 38 and now odds of because it can land on green as well odds of ball landing on black again 18 divided by 38 and now odds of because it can land on green as well odds of green or say is what two divided by 38 because there are only two grades so now if the ball lands on red for example so net gain is zero because he has used eighty five sixty one dollars over here and if it lands on black he will lose those sixty one dollars for the black bed so now same thing if the ball lands on black or red vice versa but if it lands on green he would lose all of his bet that is $61 plus $61 he would lose all of them if it if it does not land on both red and green so he will have a loss of $120 straight up so the equation would be zero gain if bet if the ball lands on red, 18 divided by 38 is of red, plus zero gain of if ball lands on black, minus if it all, if the ball lands on green, what would it be? it would be all loss, 122 multiplied by 2 divided by 38.

04:37 So this is 0 plus 0 minus 122 divided by 19...

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