+174 A bag contains five yellow balls and four blue balls. Your goal is to draw two blue balls.
You draw two balls at random. Once you have drawn two balls, you put back any yellow balls, and redraw so that you again have two drawn balls. What is the probability that you now have two blue balls?
3) a) blue x blue = 4/9 x 3/8 = 1/6
b) You could get blue x blue = 4/9 x 3/8 = 1/6
You could get blue x yellow = 4/9 x 5/8 = 5/18
Re-drawing the yellow and getting a blue = 3/8
Combining these two: 5/18 x 3/8 = 5/48
You could get yellow x blue = 5/9 x 4/8 = 5/18
Re-drawing the yellow and getting a blue = 3/8
Combining these two: 5/18 x 3/8 = 5/48
You could get yellow x yellow = 5/9 x 4/8 = 5/18
Re-drawing the two yellow and getting two blue = 4/9 x 3/8 = 1/6
Combining these two: 5/18 x 1/6 = 5/108
Adding these possibilities: 1/6 + 5/48 + 5/48 + 5/108 = 89/216
