A bag contains five white balls and five black balls. Your goal is to draw two black balls.

You draw two balls at random. Once you have drawn two balls, you put back any white balls, and redraw so that you again have two drawn balls. What is the probability that you now have two black balls? (Include the probability that you chose two black balls on the first draw.) 


I know the first case is drawing two black balls and that would be 2/9. I know the other cases would be drawing two whites and drawing one black and one white. I got \(80/59049\) i know this is not right. Can someone help plzzz. 

 Feb 2, 2020

You must consider the probability that drawing BB, BWB, WWB, or WWBB.  This gives you a probability of 2/9 + 5/81 + 12/81 + 6/81 = 41/81.

 Feb 3, 2020

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