Starting with 10 blue balls, in each of 10 sequential rounds, we remove a random ball...

Question:

Starting with 10 blue balls, in each of 10 sequential rounds, we remove a random ball and replace it with a new red ball. For example, after the first round we have 9 blue balls and one red ball, after the second round with probability 9/10 we have 8 blue balls and 2 red balls, and with probability 1/10 we have 9 blue balls and one red ball, etc.

What is the probability that the ball we remove at the 11th round is blue?

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