# statistical probability

Sanderson Smith (Sanderson_Smith@cate.org)
Wed, 27 Aug 1997 11:06:05 -0800

Aug. 27, 1997
For those who might be interested in probability and statistics examples, you
might look at the attachments (Microsoft Word 4.0). Basically, it discusses
the probability that 3 out of 67 students will have a birthday on June 1 (as
happened with the Cate School class of 1997) and compares this with the
probability of winning California Super Lotto.
Sanderson M. Smith

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n 8 of these sets we would expect to find 3 birthdays on June 1. Does this mean that this event is unlikely? The answer to this question depends upon how one chooses to define "likely" or "unlikely." In everyday useage, a probability of 0.0827% (less than 1/10 of 1%) would probability be considered unlikely. However, let's make a brief comparison to California Super Lotto, where one chooses 6 numbers from the set 1,2,3,...,49,50,51 and wins big (often millions of dollars) if the chosen 6 numbers match 6 numbers randomly selected by the State. The number of possible 6-number combinations is 51C6 =18,009,460 Your probability of matching the State's six numbers is thus 1/18,009,460. To put this in perspective, if you bought 50 Super Lotto tickets a week, you would expect to win the jackpot once every 6,900 years. Another perspective: To have a 50% chance of winning the jackpot, you would have to buy one ticket a day for 34,000 years. Simple arithmetic shows tha!
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t the probability that 3 of 67 randomly chosen birthdays will be on June 1 is over 14,000 times the probability of hitting the jackpot in California Super Lotto. Since birthdays were the original topic of discussion, it is interesting to note that if 23 people are chosen by a random process, the probability that two of them have a common birthday is 50.73%. In a random group of 67 individuals, the probability of a common birthday is 99.84%. There is no smallest among the small and no largest among the large: But always something still smaller and something still larger. -Anaxagoras (ca 450 B.C.) The " " usagean 1/10 of 1%) would probably
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