If you played roulette 36 times, each time betting $1 on a single number, then t

Question

If you played roulette 36 times, each time betting $1 on a single number, then the first two columns of the following table show how much money you would expect to profit, 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 37 distribution to calculate the probability of winning a specific 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 Winning Rounds Net Profit from X Wins Probability of X Wins with Balanced Wheel -$36 0.3729 0.3729 $0 $36 $72 0.1813 0.0571 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.) (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.)

Explanation / Answer

a.

Using MS Excel, you can find the remaining blanks in the table for the balanced wheel column: by using the syntax for second column "=A*36-36" and for third column "=BINOMDIST(A,36,(1/37),FALSE)". Then you can find:

X        Net Profit       Probability

0 -36 0.372931 1 0 0.372931 2 36 0.181286 3 72 0.057071 4 108 0.013079 5 144 0.002325 6 180 0.000334 7 216 3.97E-05 8 252 4E-06 9 288 3.46E-07 10 324 2.59E-08 11 360 1.7E-09 12 396 9.85E-11 13 432 5.05E-12 14 468 2.31E-13 15 504 9.39E-15 16 540 3.42E-16 17 576 1.12E-17 18 612 3.28E-19 19 648 8.63E-21 20 684 2.04E-22 21 720 4.31E-24 22 756 8.17E-26 23 792 1.38E-27 24 828 2.08E-29 25 864 2.77E-31 26 900 3.26E-33 27 936 3.35E-35 28 972 2.99E-37 29 1008 2.29E-39 30 1044 1.49E-41 31 1080 7.99E-44 32 1116 3.47E-46 33 1152 1.17E-48 34 1188 2.86E-51 35 1224 4.54E-54 36 1260 3.51E-57

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