Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The problem is the following: You have 10 balls:6 of them are black and 4 are white. 3 balls are removed from a box that have them,but their colors are not observed. What is the probability that the fourth ball removed is WHITE?all balls have the same probability to be removed. this last information made me get different answers...

share|improve this question
    
Ops,I´m so very sorry!!!!4=WHITE 6=BLACK.THANKS FOR NOTING!!!!!!!!!!!!!!! –  Charlie May 27 '12 at 20:03
    
Now they match. –  Charlie May 27 '12 at 20:14
add comment

1 Answer 1

up vote 1 down vote accepted

The probability is $\dfrac{4}{10}$.

Maybe think of it this way. Label the balls from $1$ to $10$, say $1$ to $4$ for the whites, $5$ to $10$ for the blacks, and mix thoroughly. Now remove the balls, one at a time. Since all orders of labels are equally likely, the probability that the $k$-th ball removed is (say) the ball with label $1$ is $\frac{1}{10}$. The probability that the $k$-th ball removed is the ball with label $2$ is also $\frac{1}{10}$, and so on. So the probability that the $k$-th ball removed is white is $\frac{4}{10}$.

The point is that any of the balls is as likely to be in position $k$ of a permutation as any other.

share|improve this answer
    
At first ,I got 2/5...please explain! –  Charlie May 27 '12 at 19:54
    
@MarylinM.J: You could be right. In the title $6$ are white. In the body, $4$ are white. In the solution I wrote out, I went with the numbers in the title. Have changed answer to go with numbers in the body. Now get $4/10$. Please change title or body so that they are consistent! –  André Nicolas May 27 '12 at 20:06
    
Oh,now i got it!I was having more work to calculate it...and for some reason i had forgot about that last information and i got different answers.THANKS ! –  Charlie May 27 '12 at 20:10
    
Just one more consideration:wouldn´t you have to considerate the fact that white balls could have been removed? –  Charlie May 27 '12 at 20:16
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.