T206 Demmitt & O'Hara....are they 350-only Series cards ?

[Matt]

Originally Posted by egbeachley

Simple statistics error. Never add or multiply the chance of something happening, rather multiply the chance something won't happen.

It's inverse so it doesn't matter - the probability it is a 350 only is the inverse of the probability it's not a 350/460. The probability is is a 350/460 is the inverse of the probability it is not a 350 only. Here it is reworded:

"To illustrate this point better, consider the inverse of your argument. Using your numbers, there is a 90% chance Demitt is not a 350/460 back and a 90% chance O'Hara is not a 350/460 back. By your logic (multiplying the probabilities), therefore, there is an 81% chance that they are not 350/460 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."

Also - didn't you multiply probabilities of something occurring?
"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."


Consider this - say Demitt was a 5 population but O'Hara showed 7 times in the survey. We can all agree then that it should be about 50/50 since Demitt would look like a 350 only card (which averaged 4.8) and O'Hara would look like a 350/460 card (which averaged a 7.4) and knowing both are the same, we couldn't use that data to say any one was more likely then the other. But multiplying the probabilities, as you have done, would lead you to the wrong conclusion:

We would have a 10% probability that Demitt would be a 350/460 series (or not a 350 only series) and say a 50% probability that O'Hara would be a 350/460 series (that percentage doesn't really matter to make the point, but assuming a normal distribution 50% is a reasonable number). So, you've got .10 * .50 = a 5% chance that they are 350/460 series and 95% chance they are 350 only series, even though we all agreed above that with those numbers it's 50/50.