Suppose box 1 contains a white balls and b black balls, and box 2 contains c white ballsand d black balls (a, b, c, d are positive integers). A randomly chosen ball is transferredfrom box 1 to box 2. Then, a randomly chosen ball from box 2 is transferred to box 1. 1. Now, if a ball is randomly drawn from box 1, what is the probabilitythat it will be white? 2. Show that if a/b = c/dthen the answer in (a) reduces to a/(a+b), i.e., it is equalto the probability of getting a white ball if we directly sample a ball from box 1without transferring. 3. Suppose the ball drawn in the end is white. Find the conditional probability that box 1 contains a white balls and b black balls (i.e., original composition)just after transferring the balls (and before sampling the last ball).
Suppose box 1 contains a white balls and b black balls, and box 2 contains c white balls
and d black balls (a, b, c, d are positive integers). A randomly chosen ball is transferred
from box 1 to box 2. Then, a randomly chosen ball from box 2 is transferred to box 1.
1. Now, if a ball is randomly drawn from box 1, what is the probability
that it will be white?
2. Show that if a/b = c/d
then the answer in (a) reduces to a/(a+b), i.e., it is equal
to the probability of getting a white ball if we directly sample a ball from box 1
without transferring.
3. Suppose the ball drawn in the end is white. Find the conditional probability that box 1 contains a white balls and b black balls (i.e., original composition)
just after transferring the balls (and before sampling the last ball).
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