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27 0.023 24 0.024 14 0.024 26 0.024 16 0.024 17 0.024 21 0.025 15 0.025 25 0.026 1 0.026 22 0.026 13 0.026 23 0.027 6 0.028 2 0.029 10 0.029 4 0.029 8 0.030 12 0.030 11 0.031 3 0.033 5 0.033 9 0.033 7 0.036 You don't have to do any fancy tests to see that these are not randomly chosen numbers. The most popular number 7 was chosen 3,176 times which would be 19 standard deviations above the mean if the numbers were randomly chosen! It is often observed that people use birthdays to choose their numbers. If they did, we would expect numbers from 1 to 12 to be most likely to be picked since such numbers can occur both in the month and the day. The next most likely numbers to be picked would be those from 13 to 31 where the remaining days of the months could occur. The least likely numbers would then be those from 32 to 45 where the year of the birthday could occur but only for those at least 52 years old. Note that this is indeed what appears to be happening. Finally, we look at the winning numbers to see if they could be considered to be randomly chosen. Recall that the lottery officials try to ensure that they are. Here we have many fewer numbers so we expect more variation even if randomly chosen. 14PDF Image | USING LOTTERIES IN TEACHING A CHANCE COURSE
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