Quote:
Originally Posted by egbeachley
For example, if 10% of the 350/460-series cards sampled as a pop 4 or 5, then there would be a 10% chance that 1 target of pop 5 would be 350/460-series. But since both targets are a pop 5, then the possibility would be 10% of 10% or a 1% chance that based on this methodology that the 2 cards are really 350/460-series.
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We're moving away from cards now, but I don't believe you are correct here (any statisticians in the house?). Multiplying probabilities to arrive at the probability that both A and B are true only works in scenarios where A and B are exclusive of each other - if A is true it has no bearing on if B is true. (i.e. the odds that both you and I have birthdays on January 1st is 1/365 * 1/365) That clearly isn't the case here as we all agree whatever is true for Demitt is true for O'Hara (i.e. the odds that twins have a birthday on January 1st is 1/365) .
To illustrate this point better, consider the inverse of your argument. Using your numbers, there is a 90% chance Demitt is a 350 only back and a 90% chance O'Hara is a 350 only back. By your logic (multiplying the probabilities), therefore, there is an 81% chance that they are 350 only backs which contradicts your finding above (of it being a 99% probability).
A such, I don't think you can multiply the probabilities in this case.
I certainly could be off with what I just wrote, so if anyone out there knows probability logic, please chime in.