(March 14, 2016 at 8:49 pm)TheRealJoeFish Wrote:(March 14, 2016 at 3:04 pm)Chas Wrote: Every combination has the same probability of occurring.
It doesn't though, and here's why:
Consider the ABCD grouping. If A picks "C" out of the hat, then when B goes to pick he'll have "A", "B", and "D" left in the hat. B can't pick his own name, so B can either pick "A" or "D". Thus, the chance that the first two picks are, say, "CD" is 1/3*1/2 = 1/6.
But, if A picks "B" on the first pick, B has "A", "C" and "D" left in the hat. So, because none of these have to be put back, B has a 1/3 chance of picking each. Thus, the chance of the first two being "BD" is 1/3*1/3 = 1/9.
That's what Rob means when he says the probability changes depending on the previous pick.
But it doesn't change the probabilities. The disallowed choices aren't part of the solution set; they simply don't exist. Their probability of being chosen is zero.
Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
Science is not a subject, but a method.