Let's find out . . .Play the Cake Walk. Each time someone plays, mark which number won. After 20 plays, look at the numbers. The chance of winning a cake is 88%. Are some numbers luckier than others? Look again after 40 plays. Are the same numbers the luckiest? Are you more likely to win a cake if you sit in the same chair every time or if you sit in a different chair every time? Suppose 7 hasn't won after 10 plays. Are you more or less likely to win if you sit in chair #7? If you did this again tomorrow would you get the same results? 
Is your Cake Walk fair?What method does your school use for choosing the winning cake?· Roll dice · Spin a spinner · Draw numbers out of a hat · Some other method If one number shows up much more often than any of the others, mathematicians say the choosing method is "unfair." US pennies are "unfair;" when you flip them they come up heads 51% of the time and tails only 49% of the time. 
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How was this table generated?This table was generated by considering your chances of losing. If the chance of losing once is: 9 out of 10 = 90% = 0.90,then the chance of losing twice is: 0.9 x 0.9 = 0.81 = 81%, and the chance of losing three times is: 0.9 x 0.9 x 0.9 = 0.729 = 73% (rounded). You can use the yx button on your calculator to calculate these numbers. Type in: . 9 (the chance of losing) yx 8 (the number of times played) = to get the chance of losing after playing 8 times. Your chance of winning is 1 minus your chance of losing. 
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How Do You Calculate Your Chance of Winning?The hard thing about calculating your chance of winning is that you don't know how many cakes you'll win. If you play 4 times, you might win 0, 1, 2, 3, or 4 cakes. Each of those chances has to be calculated separately. Also, if you win 2 cakes, you might win one the first time you played, none the second time, none the third time, and your second cake the last time you played. Or, you might lose the first two times, and win the second two times. Or . . . There are many different ways (actually 6) to win 2 cakes if you play 4 times. You have to calculate the probability of winning each way and add those probabilities together to get the probability of winning 2 cakes. To get the probability of winning at least 1 cake, you have to add the probability of winning 1 cake to the probability of winning 2 cakes to the probability of winning 3 cakes to the probability of winning 4 cakes. Let's calculate the probability of winning 3 cakes. Start at the blue circle. Follow the yellow lines. Notice that you end up at the number 3. Now, do it again with your calculator. Type in the number on the first yellow line. Now, type times. Type in the number on the next yellow line, then times again. Continue like this until you reach the 3. Then, type equals. You should get 0.0009. This is the probability of winning, winning again, then losing, and then winning. There are three other ways to win 3 cakes. Calculate them the same way, then add all four numbers together. This is the probability of winning 3 cakes if you play 4 times. Now, see if you can calculate the probability of winning 1 cake, 2 cakes, and 4 cakes. Add all these numbers together. Do they match the number on the chart? (You'll have to round.) 
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