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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.)

 Dec 1, 2019
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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.)

 

5 white, 5 black

 

\(P(BB)=\frac{5*4}{10*9}=\frac{20}{90}=\frac{2}{9}\\ P(BWB)=\frac{5*5*4}{10*9*9}=\frac{100}{810}=\frac{10}{81}\\ P(WBB)=\frac{10}{81}\\ P(WWBB)=\frac{5*4*5*5}{10*9*10*9}=\frac{500}{8100}=\frac{5}{81}\)

 

2/9+20/81+5/81 = 0.5308641975308642 

 

 

You need to check my working.

 Dec 1, 2019
edited by Melody  Dec 2, 2019

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