- posted
11 years ago

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.)

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