A bag contains two red beads and two green beads

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A bag contains two red beads and two green beads. You reach into the bag pull out a bead, replacing it with a red bead regardless of the color you pulled out. What is the probability that all beads in the bag are not red after three such replacements?
 
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What is the probability that all beads in the bag are not red after three such replacements?

Hmmm, at a guess I'd say 71.875% :)
 
I would think it is the probability of pulling out the two green beads in the first three replacement. So if my math is correct, it should be:

(2/4 * 1/4 * 4/4) + (2/4 * 3/4 * 1/4) + (2/4 * 2/4 * 1/4)
 
You could draw a tree of all the possibilities.
 

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