Posted by Kromey at 12:34am Sep 20 '07The answer is:
1/32
The reason:
With 5 red marbles and 5 black, your first marble has a 5/10 (or 1/2) chance of being red. If you do not look at that marble, it remains an uncertainty - it remains a 1/2 chance of being red. That also means that, since you still do not know what that marble is, the next marble you pick, even though you did not replace the first and thus there are only 9 marbles left in the bag, the next marble you pick also has a 5/10 chance of being red.
Until you know what color the marbles you pick are, they remain uncertainties and thus cannot be removed from the pool of possibilities. Therefore, the first marble and the 5th marble have the same probability of being red, and therefore the probability of choosing 5 red marbles is (1/2)^5 = 1/32
1/32
The reason:
With 5 red marbles and 5 black, your first marble has a 5/10 (or 1/2) chance of being red. If you do not look at that marble, it remains an uncertainty - it remains a 1/2 chance of being red. That also means that, since you still do not know what that marble is, the next marble you pick, even though you did not replace the first and thus there are only 9 marbles left in the bag, the next marble you pick also has a 5/10 chance of being red.
Until you know what color the marbles you pick are, they remain uncertainties and thus cannot be removed from the pool of possibilities. Therefore, the first marble and the 5th marble have the same probability of being red, and therefore the probability of choosing 5 red marbles is (1/2)^5 = 1/32
The much-anticipated answer! - Kromey