Question 1162401
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Note that the marble that is chosen is either red, white, or blue.  So the sum of the probabilities should be 1.  Use that to check the reasonableness of your calculations.<br>
P(A) = 2/6 = 1/3
P(B) = 4/6 = 2/3<br>
P(A,red) = (1/3)(6/11) = 6/33
P(A,white) = (1/3)(2/11) = 2/33
P(A,blue) = (1/3)(3/11) = 3/33<br>
P(B,red) = (2/3)(4/10) = 8/30
P(B,white) = (2/3)(5/10) = 10/30
P(B,blue) = (2/3)(1/10) = 2/30<br>
ANSWERS:<br>
P(red) = 6/33+8/30 = 2/11+4/15 = 30/165+44/165 = 74/165
P(white) = 2/33+10/30 = 2/33+1/3 = 2/33+11/33 = 13/33 = 65/165
P(blue) = 3/33+2/30 = 1/11+1/15 = 15/165+11/165 = 26/165<br>
CHECK: 74/165+65/165+26/165 = 165/165 = 1<br>