Question

There is a bag filled with 4 blue, 3 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 blue?

Answer 1

possible outcomes:
B,B ---- (4/12)(3/11) = 12/132
B, not blue = (4/12)(8/11) = 32/132
not blue, B = (8/12)(4/11) = 32/132
notblue, notblue = (8/12)(7/11) = 56/132
Note 12/132 + 32/132 + 32/132 + 56/132 = 132/132 = 1, as it should

so prob(exactly 1 blue out of 2 picks) = 32/132 + 32/132 = 16/33