Comments on Al Pi Cheshbon: The Probability of the Goral

Actually, I think that the "Rashi" comme...

2010-07-04T15:05:10.867-04:00

Actually, I think that the "Rashi" commentary on Bava Batra is actually written by his grandson Rashbam. So it appears from the Bach's comments. This has the advantage that Rashi is no longer disagreeing with himself in this case.

I'm on Shtikler's side. The reasonable as...

2009-07-31T03:22:11.985-04:00

I'm on Shtikler's side. The reasonable assumption is that when you stick your hand into a hat (or jar, or whatever) to pick one of a collection of similar items, it is equally likely to pick each one. So if there are three balls in a jar, we assume a 1/3 probability of picking each ball. Any probability calculation should be based on this starting point. While Anonymous has described four distinct outcomes for a certain experiment, he has not provided any reasonable explanation as to why they should be considered equally likely. And Anonymous has also not explained his claims that the various sets of events are not independent. In fact they are.

I have to respectfully disagree. I believe yours i...

2009-07-31T02:20:23.261-04:00

I have to respectfully disagree. I believe yours is the math that is flawed. The fact that you choose to halt the trial when you see that the outcome will not be "true" should have no bearing on the probability.

Look at it this way: Suppose those three people in the ball example took the balls but didn't look at them and afterwards, we look to see if they chose the correct ones. Surely, there you will agree the probability is 1/6. Are you suggesting that simply changing the manner in which you conduct the same test will affect the probability? I think that's rather preposterous.

Anyway, don't take my word for it. The omnipotent Wikipedia seems to agree. The first example they give about rolling a die twice seems to be in direct contradiction to what you wrote above.

Nice try, but your math is wrong. Each Nasi's ...

2009-07-31T02:17:23.502-04:00

Nice try, but your math is wrong. Each Nasi's draw is not an independent event, but a conditional event.
To give you an example of your flawed reasoning: suppose you had 3 balls in a jar labeled 1, 2, and 3, and you wanted to know what the probability was of persons 1, 2 and 3 selecting the ball that corresponded to the correct person (Person 1 picking "1", then person 2 picking "2", then person 3 picking "3", IN EXACT ORDER). There are only four possible outcomes: 1,2,3 ; 1,3; 2; and 3 - since once a ball is picked incorrectly, we stop. Thus the probability is 1/4. According to your math, the probability would be 1/6, which is wrong.
Put another way, what is the probability of rolling a die twice and getting a 1, and then another 1. This is NOT the same as the probability of rolling two dice and getting two 1's, which is 1/36!! These two events are not independent; the probability is 1/11.