Some casinos in Germany post archived results of roulette wheel spins for the public to examine, which we will use for the purposes of this lab. You will need to download the casino.csv dataset.+ All the data comes from Roulette Table 1, "Tisch 1", of the world famous Casino Wiesbaden from January 1, 2016 to January 31, 2016. Unlike American roulette tables, the roulette table has only one 0 slot (colored green), and the numbers 1 through 36 alternating black and red. The data has been slightly modied and simplied for the purposes of this assignment. Each row in the le corresponds to a single roulette wheel spin. . spinOutcomethe number the ball landed on at the roulette table - datethe date the spin was made Roulette is a simple game. The wheel is spun, a ball is released, and the ball eventually lands on a number. One of the simplest bets to make is to bet on a single number. If you win, you get 35 times your original bet, plus your original bet back. In casino jargon, the payout is "35 to 1" or "35:1", because if you bet $1 you get $35 from the dealer, plus you get back your original bet amount, for a prot of $35. when you lose, you get nothing back, so your prot is $1. It is possible to bet on more than one number during a roulette wheel spin, increasing your chances of "winning" on at least one bet (even though you may end up losing more money, since you have to place more bets). 3 El Tech Guide You will need to use the SPSS Tech Guide. ' El Lab Questions Suppose you wanted to guarantee that you would win on at least one number for one roulette wheel spin. Imagine betting a dollar on every red and every black number (1 through 36), and also on the green 0. (a) In order to place all of your bets, how much would you have to spend? $37 (b) Since you bet on all the possible outcomes, you are guaranteed to win a single bet. What is the total paid back to you (that includes any winning bet amount that you got back)? $ 36 J (c) How much is your total prot/loss? (Hint: Prot = Revenue Expenses)? $4 J (d) Another way of thinking about this betting scenario is in terms of prots or losses per bet. You made 37 bets. What is the prot on the single bet that won? $ 35 'I What is the prot for each of the 36 bets that lost? 35 -1 u/ You, along with a group of opportunistic gamblers, notice a pattern of numbers that seem to come up more frequently than expected on Roulette Table 1, "Tisch 1". (a) A bar graph ls just a bar showing how many data points from each category your data contains, and the bars are not required to touch one another. If you create a frequency histogram, the bars do touch each other, and the rst bar will range from 0.5 to 0.5 (even though It only represent: the discrete number 0 on the roulette wheel). The second bar of the frequency histogram will range from 0.5 to 1.5 (representing the number 1 on the roulette wheel). To create a frequency histogram, you will therefore have to specify that the bars start at the number 0.5, and make each bar have a width of 1. Create and upload a bar graph or a frequency histogram of the outcomes from Table 1. (Submit a le with a maximum size of 1 MB.) Choose File No le chosen frequency histogrm .docx Score: 0.04 out of 0.04 Comment: (b) which three numbers seemed to come up very frequently? smallest value N1 = 26 N2 = 29 largest value N3 = 31 v Assuming that the wheel is biased in favor of the three numbers, use the results of the January data to create estimates of the probability for each of those three numbers. (Round your answers to ve decimal places.) P(N1) = .03525 x P(N2) = .03434 P(N3) = .03775 X X If you played roulette 36 times, each time betting $1 on a single number, then the rst two columns of the following table show how much money you would expect to prot, depending on how many times you won out of the 36 trials. (a) For a perfect wheel, the probability of getting a single number on a spin is % = 0.02703. You can use the binomial distribution to calculate the probability of winning a specic number of times out of 36 rounds. For example, the probability of winning two times out of 36 rounds is 0.1813. Use this example to verify that your software is working correctly. Fill in the remaining blanks in the table for the balanced wheel column. (Round your answers to four decimal places.) X, the Number of wlnnlng Rounds Net Profit from X Wlns Prohablllty of X wins with Balanced wheel 0 $36 .3729 2 $36 0.1813 3 $72 0571 . . . . . . 36 $1,260 3.505 x 10-57 (b) Using the table, calculate the probability of losing money or just breaking even for the balanced roulette wheel. (You will need to add together two rows of the table above. Round your answer to four decimal places.) 0.7458 (c) You know that all the probabilities have to add up to 1. Use the probability calculated in part (b) to calculate the probability of walking away with a net profit (better than break-even). (Round your answer to four decimal places.) 0.2542 (d) Using the biased wheel, "Tisch 1", it was determined that the probability for one of the numbers was about 0.03776, which is higher than normal. Suppose you bet on this number for 36 rounds. Use this probability to fill in the blanks in the biased wheel column. (Round your answers to four significant figures.) X, the Number of Winning Rounds Net Profit from X Wins Probability of X Wins with Biased Wheel 0 -$36 .2502 V $0 .3534 V 2 $36 .2427 V W $72 . 1079 V . . . . . . . . . 36 $1,260 0 Xfour decimal places. ) 0.7458 (c) You know that all the probabilities have to add up to 1. Use the probability calculated in part (b) to calculate the probability of walking away with a net profit (better than break-even). (Round your answer to four decimal places.) 0.2542 (d) Using the biased wheel, "Tisch 1", it was determined that the probability for one of the numbers was about 0.03776, which is higher than normal. Suppose you bet on this number for 36 rounds. Use this probability to fill in the blanks in the biased wheel column. (Round your answers to four significant figures.) X, the Number of Winning Rounds Net Profit from X Wins Probability of X Wins with Biased Wheel 0 -$36 2502 $0 .3534 2 $36 .2427 V W $72 .1079 V . . . . . . . . . 36 $1,260 0 X Calculate the probability of walking away with a net profit (better than break-even). (Round your answer to four decimal places.) 7.5021 X