Probability: Drawing Marbles

Question

There are 2 blue marbles, 3 green marbles, and 5 purple marbles in a bag randomly mixed. If you draw three marbles one at a time without replacement, what is the probability of drawing one blue, one green, then one purple?

Answer 1

There are 10 marbles in the bag and 2 blue, so the probability of drawing the blue is 2/10 = 1/5. Then, there are 9 marbles remaining in the bag. The probability of drawing a green is 3/9 = 1/3. After that there are 8 marbles remaining so the probability of drawing a purple is 5/8.

The desired probability is then (1/5)(1/3)(5/8) = 1/24.