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Discrete Mathematics and its Applications
Found in: Page 452
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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Short Answer

Question: Show condition (i) and (ii) are met under Laplace's definition of probability, when outcomes are equally likely.

Answer

Condition (i) and (ii) are met under Laplace's definition of probability when outcomes are equally likely.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Given data

Let S be the sample space of an experiment with a finite or countable number of outcomes. P(s) Be the probability of each outcome S .

Condition :

0⩽P(s)⩽1 For each s∈S.

This states that the probability of each outcome is non negative real number which is no greater than .

Condition (ii) :

∑s∈SP(s)=1

This states that the sum of all probabilities of all possible outcome should be 1 .

Step 2: Concept used Laplace’s formula

Generalization of Laplace's definition in which each n outcomes is assigned a probability of 1n .

Step 3: Solve for probability

The conditions(i) and (ii) are satisfied when the Laplace's definition of the probability of equally likely outcomes is used and S is finite.

Hence, when there are possible outcomes x1,x2,xn the two conditions are to be satisfied.

0⩽P(s)⩽1 for i=1,2,………...n∑i=1nPxJ=1

The function from the set of all outcomes of the sample space S is called the probability distribution. Conditions (i) and (ii) are met under Laplace's definition of probability when outcomes are equally likely.

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