Question 1025391: An urn contains 5 yellow balls and 4 green balls. A ball is drawn randomly; it is not put back but another ball of the opposite color is put into the urn into place.This process is repeated 2 or more times. Let Y1= Event the ball is yellow and let G1= even the ball #1 is green.
Find all of the following:
a. Pr (Y2|Y1)
b. Pr(Y2|G1)
c. Pr (Y3|Y1,& Y2)
d. Pr (Y3|Y1&G2)
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! a. Given the first ball drawn was yellow (Y1), the urn now contains 4 yellow balls and 5 green balls. Hence P(Y2|Y1) = 4/9.
b. Given the first ball drawn was green (G1), the urn now contains 6 yellow balls and 3 green balls. Hence P(Y2|G1) = 6/9, or 2/3.
c. Given the first ball drawn was yellow (Y1) and the second ball drawn was also yellow, the urn now contains 3 yellow balls and 6 green balls. Hence P(Y3|Y1∩Y2) = 3/9, or 1/3.
d. Given the first ball drawn was yellow (Y1) and the second ball drawn was green, the urn now contains 5 yellow balls and 4 green balls. Hence P(Y3|Y1∩G2) = 5/9.
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