"Ignoramus27678" wrote in message
...

On 2011-11-06, Bob Engelhardt wrote:
Given: an opaque jar with a large number of white & black marbles, same
number of each. If I pick 2 marbles randomly, it seems that the
probabilities depend upon how I do the drawing.

If I pick one marble, then pick another, the probability of drawing one
black and one white marble is 50%. (4 possibilities, 2 of which give 1
white & 1 black.)

If I reach in and pick 2 marbles AT ONCE, the probability is 33%. (3
possibilities, 1 of which gives 1 of each color.)

3 possibilities, unequal probabilities.

Your reasoning is wrong.

i\

Jeez, you're harsh. d8-) Why don't you explain that the two possibilities of
one each black and white, in the first example, actually give the same
result and are really just two different orders for the *same*
possibility -- one white, one black?

Inelegant, but maybe helpful...

--
Ed Huntress




It just doesn't SEEM right that the probabilities could be different.
Why is it different? Or is it not different? Is there really 4
possibilities when drawing 2-at-once?

Drawing 3 marbles gives even worse results. One-at-a-time gives:
1/8 probability of all black,
1/8 all white,
3/8 2 black + 1 white, &
3/8 2 white + 1 black.

3 at once gives:
1/4 all black,
1/4 all white,
1/4 2 black + 1 white, &
1/4 2 white + 1 black.
The probability of drawing all same color 3-at-once is twice that of
one-at-a-time!

Is there a statistician in the house?

Bob