Question

Draw a probability tree diagram for the following experiment: Suppose there are five balls in an urn. Three are red and two are blue. We will select a ball, note the color, and, without replacing the first ball, select a second ball. What is the sample space of this

experiment? What is the associated probability distribution in this

experiment?

Answer 1

Let R : event of selecting red ball

B : event of selecting blue ball

Sample Space : RB     RR   BB   BR

Finding probabilities for each item in sample space

P(RB) = P(select first red ball x select second blue ball)

              (2nd ball is without replacing the first ball, hence denominator is 4)

              (Second fraction 2/4 is for the second red ball. as total red balls reduce from 3 to 2

                                                                 before drawing the second ball)

Probability Distribution

Sample Space	RB	RR	BB	BR
Probability	0.3	0.3	0.1	0.3

Probability Tree Diagram