Question

A box contains 8 blue marbles, 4 red marbles, 3 green marbles.
A. if three marbles are selected at random, what is probability that all three marbles will be blue marbles
B. if three marbles are selected at random, what is the probability that one of each color marble will be selected.

Answer 1

There are  B = 8    R = 4    G = 3      total = T = 15

A)
   Let three marbles be chosen one after another.  It does not matter we select one after another or all three marbles at the same time, as long as we do not look at them till we have all three.  We use the conditional probability formula for dependent events  A and B.
              P ( B ) = P(B/A) * P(A)
 
   P ( Blue, Blue, Blue) = B / T  * (B-1) / (T-1)  * (B-2) / (T-2)
                   =  8/15 * 7/14 * 6/13  = 8 / 65

B)
     There are six possible ways in which this can happen.
     The selections can be : BRG, BGR, RBG, RGB, GBR, GRB - in this order.  But which ever order of selection we choose the probabilities will be, for each of them :
         B/T * G/ (T-1) * R / (T-2)  or   B*G*R / [ T (T-1)(T-2) ]

   So the answer is =  6 *  (8 * 4 * 3) / [ 15 * 14 * 13 ] = 96/455