Conditional Probability!!!

[harbinger]

Box 1 contains 1 white and 999 black balls, box 2 contains 1 black and 999 white balls. Randomly pick a ball from randomly selected box. Provided it is a black ball. What is the probability that the ball is picked from box 1?
Thanks.

[fmku]

This page has an exact similar question along with explanation http://www.netnam.vn/unescocourse/statistics/46.htm

Since it is given that the ball is picked from Box 1 therefore after that we had only fing the probability in that.
P(B in A1) = 999/1000

[queen_viola]

fmku .....this is an excellent site ! thx ! do you know of any other good site on prob , permutation and combination (maths prob) etc ?

[profiler]

excellent site :-) fantastic......
but the probability questions u get in actual GMAT is way way above these questions :-(

[GREPrep]

Ans = 0.495

[Big Dog 04]

^^^ Yep sounds right to me.

[fmku]

Ans = 0.495

How Please explain.

[Commentor]

Ans = 0.495

So you mean that the probability is less than 1/2 ?!

P(chosen from box 1 | provided it is a black ball) = P(it is a black ball from box 1) /
P(it is a black ball) = 999/2000 / 1/2 = 999/1000 = 99.9% = quite sure that it's from the first box.

P(A|B) = P(AB) / P(B) by definition!
What does it mean? "provided it is a black ball"?
Imagine all 2000 cases.
Only in 1000 cases it is a black ball. And in 99.9% it is from the first box.


There is a famouse question illustrating the idea.
There are two "coins" (or flat circles): one is entirely white, another is entirely red, and the first one has one white and one red side.
Somebody chooses random coin (out of three) and then shows you it's random side.
It is red. Then what is the probability that the other side is red too?

(There's some complication then when he shows you one side the other is either red or not red so the answer is 0 or 1. Don't think about it We talk about future events - "in case one side...").

[rishanthchavali]

please be precise in your explanation....can u please reduce your solution to few steps.....

[thepillow]

Ans = 0.495

In my opinion 0.495 is not the correct probability. The answer should be 0.999. (Although many other conditional probability problems do yield seemingly strange results).

Here's why:

We're asked to figure out the probability that the the black ball selected was from box 1. The way to calculate this is to figure out the number of ways that a black ball can come from box 1 and then divide by all the ways of getting a black ball.

We can see this clearly by making a tree diagram: