Chapter 2, Problem 2.1P

A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble from the box and then replacing it in the box and drawing a second marble from the box. Describe the sample space. Repeat when the second marble is drawn without replacing the first marble.

To determine

To find: The sample space of given experiment with replacement and without

replacement.

Answer to Problem 2.1P

The sample space with replacement

$=\{(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)\}$

The sample space without replacement $=\{(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)\}$

Explanation of Solution

Given information:

Consider box contains three marbles. They are $1$ Red marble $(R)$ , $1$ Green marble $(G)$ , $1$

Blue marble $(B)$ .

Calculation:

Sample space is the set of all possible outcomes of a random experiment.

Consider the experiment of drawing two marbles one after another with replacement.

Total number of outcomes $=3^2$

Then, the sample space is given by

$=\{(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)\}$

Consider the experiment of drawing two marbles one after another without replacement.

Total number of outcomes $=3\times 2=6$

Then, the sample space is given by $=\{(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)\}$