Oooo, can I play?
The probability in any one year that 1 of the top 10 wait-listed students is in one the 50 3rd grade classrooms is 1/5 = 20%. (assuming random distribution)
For each subsequent year, the probability increases that you've had one at least once.
Year 2 = 36%
Year 3 = 48.8%
Year 4 = 59.04%
Year 5 = 67.23%
...
Year 25 = 99.62%
For one of the top 25 wait-listed students:
Year 1 = 50%
Year 2 = 75%
Year 3 = 87.5%
Year 4 = 93.75%
Year 5 = 96.88%
...
Year 25 = 100% (almost!)
Now, the chance of having 2 of the top 10 in one year is 4%. After 4 years, the chance of her having had 2 of the top ten at least once is 15%.
3 of top ten in one year .8%, after 4 years 3.2%.
Extra Credit:
With normal distribution, you would expect approx. 1/44 people to have IQ 130+. So of 1300 kids, 30 should be 130+. Approx. 1/261 have 140+. 5 of 1300.
Most likely a higher percentage than above in your area, but still not 50 kids 140+.
HTH. Either way, it sure was fun!
