Chapter 4.1, Problem 1E

To determine

To find:

The sample space for the given experiment.

Answer to Problem 1E

Solution:

The sample space when two coins are tossed is

$S=\left\{HH,TH,HT,TT\right\}$

Explanation of Solution

Given:

An experiment of tossing two coins.

Approach:

A probability experiment (also called random experiment) is defined as any process whose outcome can be any one of all the possible outcomes, which depends entirely on chance. An outcome is defined as the result of the experiment. A set of all possible outcomes of an experiment is called a sample space.

There are only two possible outcomes in tossing a coin, i.e. heads or tails. Let the occurrence of a head be denoted by ‘H’ and the occurrence of a tail be denoted by ‘T’. When two coins are tossed, there can only be four possible outcomes – both the coins show heads, 1^st coin shows head and 2^nd coin shows tail, 1^st coin shows tail and 2^nd coin shows head, and both the coins show tails. Therefore, the sample space (denoted by S) becomes,

$S=\left\{HH,TH,HT,TT\right\}$