Consider an urn which contains red balls and green balls. Initially there is just one green ball and one red ball in the

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Consider an urn which contains red balls
and green balls. Initially there is just one green ball
and one red ball in the urn. At each time step a ball is chosen
randomly from the urn: (i) If the ball is red, then it’s returned
to the urn with an additional red ball; (ii) if the ball
is green, then it’s returned to the urn with
an additional green ball.
Let ​Xn​ denote the number of red balls
in the urn after ​n draws. Suppose after 100
draws, there are 70 red balls, that is X100​=70. What is
the expected number of red balls in the urn after another 100
draws, that is E[X200​∣X100​=70]? Round your
answer to the nearest integer.