C D E M R w Z AB A W N = S L O V Q UI A F G H N AA AC DUNE Bet Coin Flip # H in a Row Winnings You are going to flip a coin and bet on Tails coming up. You start with a $10 bet and will double your bet if you lose; once you win you revert to the $10 bet. This guarantees you a profit! $10.00 a.) We will complete the first row and then the second row. Enter an IF function in cell C6 that "flips a coin" with equal probability of getting an H or T. b.) Enter an IF function in cell D6 that returns 1 if the first flip is H, else it returns 0. .) Enter an IF function in cell E6 that returns $10 if the first flip is T, else it returns -$10. Format as currency with two decimal places. d.) Now for the second row. Enter an IF function in cell B7 that returns $10 if the first flip is T, else it doubles the previous bet e.) Fill down the IF function in cell C6 to C155. f.) Now for the # H in a row. Enter an IF function in cell D7 that returns 0 if the flip is T in the 2nd row, else it adds 1 to the previous number in cell D6. Fill cell D7 down. g.) Finally we compute the Winnings. Enter an IF function in cell E7 that adds the current Bet to the previous Winnings if the flip is T in the 2nd row, else it subtracts the current Bet from the previous Winnings. Fill cell E7 down. Max # H in a Row: Probability: h.) Compute the Max # H in a Row and use the 1st Law of Probability to compute to three decimal places the probability of flipping a Expected # in 150: FEE fair coin and getting that many heads in a row (your formula should link to the Max # H in a Row cell). Finally, use this probability to compute the expected number of times you would get this many # H in a row in 150 flips. Max Bet: Max Winnings: i.) Compute the Max Bet and Max Winnings formatted as currency with 2 decimal places. Gambler's Ruin j.) By doubling your bet when you lose, you can guarantee that your winnings will always increase. Find a place where you go on a Winnings Increase by: "losing streak", meaning you get a streak of H's in a row. Make note of your winnings before you start flipping the H's. Eventually you ZE will flip a Tails and win your bet. This increases your winnings from before the losing streak started by how much? Ruin? k. k.) So, if you can guarantee to increase your winnings, why is this called "gambler's ruin"? 1. Your max bet required might get larger than you can cover. 2. It would take too long to play the game 150 times. It goes all the way to 150 In cell C6, use the IF and nested RAND functions to flip a coin for the first time. Note: Use "H" for head and "T" for tail in the arguments of the IF function. In cell D6, use the IF function that returns 1 if the first flip is H, else it returns 0. In cell E6, use the IF function that returns $10 if the first flip is T, else it returns -$10. Format cell E6 as Currency with 2 decimal places. In cell B7, use the IF function that returns $10 if the first flip is T, else it doubles the previous bet. Fill cell B7 down the column to cell B155. Format cells B7:B155 as Currency with 2 decimal places Fill cell C6 down the column to cell C155. In cell D7, use the IF function that returns 0 if the flip is T when you flip the coin for the second time, else it adds 1 to the number in previous cell in column D (i.e., the IF function in cell D7 should refer to cell D6). Fill cell D7 down the column to cell D155 In cell E7, use the IF function to determine the winnings when you flip the coin for the second time. Fill cell E7 down the column to cell E155. Format cells E7:E155 as Currency with 2 decimal places. In cell J27, calculate the maximum number of H in a row. In cell J28, calculate the probability of flipping a fair coin and getting that many heads in a row determined in cell J27. Format cell J28 as Percentage with 3 decimal places. In cell J29, calculate the expected number of times you get the maximum number of H in a row in 150 flips In cell J32, use the MAX function to determine the maximum bet at 150 flips. Format cell J32 as Currency with 2 decimal places. In cell J33, use the MAX function to determine the maximum winnings at 150 flips. Format cell J33 as Currency with 2 decimal places. In cell J36, determine by how much your winnings increase from just before the losing streak starts to right after it ends. In cell J39, determine the reason why this is called "gambler's ruin&quot