What is the probability of drawing, in order, 2 red, 1 blue, and 2 yellow marbles if a bag contains 4 yellow, 5 red, and 6 blue marbles?

Oct 29, 2014

I assume that marbles are not returned after drawn here.

Draw 1: 5 reds out of 15 marbles: $\frac{5}{15}$
Draw 2: 4 reds out of 14 marbles: $\frac{4}{14}$
Draw 3: 6 blues out of 13 marbles: $\frac{6}{13}$
Draw 4: 4 yellows out of 12 marbles: $\frac{4}{12}$
Draw 5: 3 yellows out of 11 marbles: $\frac{3}{11}$

Hence, the probability is

$\frac{5}{15} \cdot \frac{4}{14} \cdot \frac{6}{13} \cdot \frac{4}{12} \cdot \frac{3}{11} = \frac{4}{1001}$

I hope that this was helpful.