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Q. 2.1

Expert-verified

A First Course in Probability

Found in: Page 48

Book edition 9th

Author(s) Sheldon M. Ross

Pages 432 pages

ISBN 9780321794772

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Short Answer

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.

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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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 $R$ represent the red marble, $G$ represent the green marble and $B$ represent the blue marble.

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 $3 \times 3$ . Since, there are three possibilities for the first draw and three possibilities for the second draw.

Thus, the sample space is:

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

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 $3 \times 2$ . 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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