help with a probability question

Question

An urn contains 5 yellow balls and 3 green balls. A ball is drawn randomly. In its place one of the other colored balls is added to the urn. Let Yi; and Gi respectively be the event that ball number I is yellow, green.

Find all of the following
a) Pr(Y2|Y1)
b) Pr(Y2|G1)
c) Pr(Y3|Y1Uy2)
D)Pr(Y2|Y1UG2)

Answer 1

Since one ball is drawn and one is replaced there will always be 8 balls in the urn.

 

a) after drawing Y1, the urn will contain 4 yellow and 4 green.  Pr(Y2|Y1) = 4/8 or 1/2

 

b) after drawing G1, the urn will contain 6 yellow and 2 green. Pr(Y2|G1) = 6/8 or 3/4

 

c) after drawing Y1, and then Y2, the urn will contain 3 yellow and 5 green. Pr(Y3|Y2uY1) = 3/8

 

d) after drawing Y1, and then G2, the urn will contain 5 yellow and 3 green. Pr(Y3|G2uY1) = 5/8

 

   Note if Y2 means that the second ball drawn is yellow; then Pr(Y2|Y1uG2) = 0  since the second ball drawn was a green.