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Posted By: Glenn

Ted,

I have all the respect in the world for AT&T EE's. My own father has been an AT&T EE for the past 32 years. I have never been an engineer, but I have been a statistics professor, and your claim that the presence of only 3 Paiges in the group of 576 defies all laws of statistical probability is demonstrably false.

It takes neither a statistician nor an engineer, merely an 8th grade student, to determine that there will be an average of 12 of each card if there are 576 total of 48 different types. Averages are easy to calculate; it's variances that get confusing. Obviously there will be some variation in the numbers; that is, not every card will have exactly 12 just because the average is 12. So we will expect there to be fewer than 12 of some and more than 12 of others. (This is true whether there are equal numbers of each card in the total production run or not.) One (or more in case of a tie) of the 48 cards will be the least frequent in your sample, and another (or others) will be the most frequent.

The probability that any one PARTICULAR card will have exactly 3 examples in the sample of 576 is 0.177%. The probability that there will be a card (any of the 48) that occurs with this fequency is just 48 times this number: 48 x .177% = 8.5%. So even if all the cards were produced in exactly equal numbers, and all the cards were distributed in packs completely at random, there is an 8.5% chance that the card that turns up least frequently in your sample of 576 cards will only turn up 3 times.

This is the same as the probability that a .292 hitter will get hits in both of his first 2 at-bats of a game, certainly not probable but neither is it defiant of any laws of probability of which I am aware.