That's only true if betting/guessing on any individual flip. Then, the probabilities are unrelated. Regardless of what it landed on last time, is indeed still 50/50 with each flip. But that has zero to do with what I was talking about with figuring probability off the statistics given. That's not how it is calculated in this situation.
Using your example of a coin, a joint probability differs when one makes a statement that they will flip a penny and it will come up heads 3 times in a row. Then it becomes a joint probability, in which case, the odds become multiplicative .5 x .5 x.5 so the odds of the penny coming up heads 3x in a row, if stated as such is 12.5%.
With regard to the erroneous use of statistics based on the logic as applied to the article of moving from 55% pre-rejection, to 44.4% on time 2, that is a joint probability, because now you include two events to determine one dichotomous outcome, accepted or not accepted. In such case, you must exclude the 100% sample, and only use the 45% left in applying the additional 20% that was initially given using a denominator of 100.
Sorry...but your argument is flat out wrong JJ. That's not how statistics and the calculation of probability works.
Maz
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