Question

A box contains 5 red balls and 3 yellow balls. If 4 balls, one at a time will be drawn at random from the box without replacement. What is the probability that the balls alternate in colors?

Answer 1

Probability of drawing a red ball is 5/8 and for a yellow ball is 3/8. We shall find this probability using a tree diagram.

From the tree diagram above, we consider the sample space containing alternating colors, that is

P(RYRY) and P(YRYR), then sum their probabilities.

P(RYRY)=5/8*3/7*4/6*2/5=120/1680

P(YRYR)=3/8*5/7*2/6*4/5=120/1680

Summing both probabilities

120/1680+120/1680=240/1680

=1/7.

Therefore, the probability that the balls alternate in color is 1/7