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15 Figure 4. Since there were 508 drawings in the period we are considering, we have 6 × 508 = 3048 numbers. Now, if the numbers are randomly chosen, the number of times a particular numbers occurs has a binomial distribution with n = 3048 and p = 1/45. Such a distribution has a mean of 67.7 and standard deviation 8.14. The biggest deviations from the mean are about 2 standard deviations so this looks consistent with the hypothesis that the numbers were randomly chosen. Again, we could check this with a ChiSquare test. FINDING PATTERNS Recall that players choose their first five numbers to match the white balls separately from their choice of the Powerball number to match the red ball. Thus, if we are looking for patterns in the way people choose their numbers, it is best to consider the first five numbers by themselves. For comparison, we again consider the 17,001 picks chosen by the Easy Pick method and by the players. For the Easy Picks, we found that 136 of these were represented twice and 2 were represented 3 times. To see if we should have expected to find 3 picks the same, we again apply a result from the appendix to estimate the number of people required to have probability p of finding k or more with the samePDF Image | USING LOTTERIES IN TEACHING A CHANCE COURSE
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