Probability puzzle -- 50% or one in ten?

Question

An urn has 10 marbles. One is black, nine are white. A marble is removed, one at a time, without replacement. The first 8 marbles removed are all white. What is the probability of picking the black marble? Is it 50% or 10%? Why?

Answer 1

Review on probability, here you have discrete probability,
for prob of black is 0.1
prob of white is 0.9

even though they sum up to be 1.0 but its not binomial distribution. By means of binomial distribution, you got to have fixed n observations, with each independent and each probability must have the same chances of being chosen.
Here, once you have the first 8 marbles chosen, the probability of choosing white and black is changing.

Out of ten, now you have only 2 marbles left and with each can be chosen at the next ball, its not 0.1 or 10% for the black. It is 1/2 or 0.5 or 50%.

If you need review on binomial distribution, let me know

Answer: 50%

*still confused? write back

Answer 2

It's 50% because there are 10 marbles minus the 8 marbles he drew which were all white, and since there is only 2 left, there's a 50% chance of drawing a black

Answer 3

The Answer would be 10%. If the info is put into a fraction, black probability is 1/10, and white probablity 9/10. However, as you pull each one out, it decreases it. Because the first eight are white, then that decreases the white probablity in the numerator to be 1, and the black probability in the numerator to be 1. However the deciding factor between the answers is that the marbles are not replaced. This means they are removed from the denominator of each. This makes each probability 1/2, or 50%.

Answer 4

At this point, considering that you are only picking among the marbles left in the urn, the chance of picking the black marble is 50%, because there are two left, and exactly 50% of those two are black.

Answer 5

50% because there are only 2 marbles left. it was 10% at the beginning but as the whites were picked the chances of drawing a black marble increased.

Answer 6

Since there are only two marbles left in the urn, and one of them is black, then there's a 50% chance of getting a black one in the next draw.

Answer 7

50% - if there are only two left and you know the only ones removed have been white.. there is one white and one black marble left in the urn, so it's a 1/2 or 50% chance you'll pick the black one.

Answer 8

when ten marbles were in there, you had a 1 in 10 chance or 10%
but, now that their is only 2, you have a 50/50 chance of getting it or 50%

Answer 9

50%, the chance of picking the black marble next is 1 in 2, independent of any previous picks.

Answer 10

50%

There are only 2 marbles left, one is the black one.
1 divided by 2 is 50%.