Using R code. Urn 1 contains three white balls and two black balls. Urn 2 contains one white ball and three black balls. A ball is selected at random from Urn 1 and transferred to Urn 2. Next, a ball is selected at random from Urn 2 and transferred to Urn 1. Finally, a ball is selected at random from Urn 1. Use simulation to estimate the probability that the ball selected on this third draw is black with n = 10^6 iterations and the initial seed 3700.

(Hints: 1. Use for() loop, sample(), if(), vector for urn1 and urn2. 2. Derive the theoretical result to confirm your simulation output.)