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Chapter 2: Q. 2.1 (page 48)

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.

Short Answer

Expert verified

The sample space of drawing one marble with replacement is(R,R),(R,G),(R,B),(G,R),(G,G),(G,B),(B,R),(B,G),(B,B)

The sample space of drawing one marble without replacement is(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)

Step by step solution

01

Step 1. Given information.

It is given that,

Total no. of marbles =3

No. of Red Marbles=1

No. of Green Marbles=1

No. of Red Marbles=1

Let Rrepresent the red marble, Grepresent the green marble and Brepresent the blue marble.

02

Step 2. Find the sample space of drawing one marble with replacement.

The sample space consists of all possible results of this experiment.

Let us assume that the red ball is drawn first, the second ball can de either red, or blue, or green and so on.

The size of sample space will be 3脳3. Since, there are three possibilities for the first draw and three possibilities for the second draw.

Thus, the sample space is:

(R,R),(R,G),(R,B),(G,R),(G,G),(G,B),(B,R),(B,G),(B,B)

03

Step 3. Find the sample space of drawing one marble without replacement. 

The sample space consists of all possible results of this experiment.

Let us assume that the red ball is drawn first, the second ball can de either blue, or green and so on.

The size of sample space will be 3脳2. Since, there are three possibilities for the first draw and two possibilities for the second draw.

Thus, the sample space is:

(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)

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