Question

A bucket contains 4 red balls and 5 orange balls. Two balls are pulled from the bucket, one after another, without replacement. Build a tree diagram showing the different possible outcomes for the two marbles being drawn. Be sure each branch is labeled with its individual probability and include the probability at the end of each branch.

Answer 1

See the diagram below:

Red 3/8 -----------------> Red-Red = 4/9*3/8 = 1/6

Red 4/9 <

Orange 5/8 --------------> Red-Orange = 4/9*5/8 = 5/18

Red 4/8 --------------------> Orange-Red = 5/9*4/8 = 5/18

Orange 5/9 <

Orange 4/8 ----------------> Orange-Orange = 5/9*4/8 = 5/18