What can I say?

If you analyze a probability problem start to finish and add in the assumption that the outcome you saw is the only possible outcome that could have happened, then you'll usually get wrong answers. That isn't a matter of opinion - that's mathematical fact.

In case you're curious, here's how the formal approach goes. You start with a priori estimates of various scenarios. You run the experiment and see what happened. You then compute the conditional probabilities of the scenarios of interest given what just happened using the well-known formula from Mr. Bayes, P(A|B)=P(A and B)/P(B). In English that says, "The probability of A given that B happened is the initial probability that A and B both happened divided by the initial probability that B happened." That gives you the right numbers every time. Any other approach can only be right when it winds up agreeing with that one.

Look elsewhere in this thread for the problem that was misstated in tye's textbook about how likely the other child was a daughter. And try to understand the full (if informal) analysis that I gave. You should see how a correct analysis has to consider what might have happened (but didn't). Furthermore you'll see how very subtle differences in the stated problem change what was possible, and result in very different estimates. (Note that I didn't pull out the formal machinery. I would have needed to if I wanted to show how to adjust the answer to account for the fact that about 51% of children are male.)

If you still think that I'm wrong, well that is your perogative. I've spent all of the energy on this thread that I'm willing to spend. I'm not here to present a course on elementary probability theory. You're not here to take one. So I'll let it drop here.

In reply to Re^9: Marilyn Vos Savant's Monty Hall problem by tilly
in thread Marilyn Vos Savant's Monty Hall problem by mutated

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