Suppose an urn has b blue balls and r red balls. We randomly pick a ball. If the

Question

Suppose an urn has b blue balls and r red balls. We randomly pick a ball. If the ball
is red, we put two red balls back to the urn. If the ball is blue, we put two blue balls back to the urn. Then we randomly pick a ball again.
(1) What is the probability that the rst pick is red?
(2) What is the probability that the second pick is red?
(3) (Optional) If we continue, then what is the probability that the third pick is red? Suppose an urn has b blue balls and r red balls. We randomly pick a ball. If the ball
is red, we put two red balls back to the urn. If the ball is blue, we put two blue balls back to the urn. Then we randomly pick a ball again.
(1) What is the probability that the rst pick is red?
(2) What is the probability that the second pick is red?
(3) (Optional) If we continue, then what is the probability that the third pick is red?

Explanation / Answer

If you have one green block to start with and then I give you a blue block, you have two total blocks. I can't think of any type of proof besides that type of argument.

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