probability

Question

A bag contains 8 red marbles, 5 blue marbles, 10 white marbles and 8 yellow marbles. You are asked to draw 5 marbles from the bag without replacement. What is the probability of drawing more than 4 yellow marbles?

Answer

Answer 1

There are 8+5+10+8=31 marbles in the bag. If 5 marbles are drawn without replacement, and more than 4 yellow ones are drawn, then all 5 marbles must be yellow.

1st draw: probability=8/31; 2nd draw: probability=7/30; 3rd draw: probability=6/29; 4th draw: probability=5/28; 5th draw: probability=4/27.

Combined probability:

(8/31)(7/30)(6/29)(5/28)(4/27)=(7/28)(6/30)(4/27)(5/29)(8/31)=

(1/29)(1/27)(8/31)=8/24273=0.0003296 approx=0.033% approx.