Question

Match the followings. Here, ELE stands for $\text{equally likely event}$.

• A. $0$
• B. $\frac{1}{2}$
• C. $1$

Answer 1

$\underset{–}{\text{Certain Event}}$ An event is said to be a $\text{Certain Event}$ if there is an absolute surety on its occurrence. The probability of certain event is always equals to 1. $\text{Example:}$ When a fair die is rolled, getting a natural number less than $7$, is a certain event.

$\underset{–}{\text{Impossible Event}}$ An event that has no chance of occurring is called an $\text{Impossible Event}$. The probability of an impossible event is always zero. $\text{Example:}$ When a fair die is thrown once, the event of getting a number greater than 6, is an impossible event as the highest number on a die is $6$.

$\underset{–}{\text{Equally Likely Event}}$ An event is said to be $\text{Equally Likely}$ if there is equal chances of its occurance and non-occurence. The probability of equally likely event is $\frac{1}{2}$. $\text{Example:}$ Tossing head or tail on a fair coin is individually an equally likely event as both the probabilities of occurrence and non-occurrence of tossing head or tail is $\frac{1}{2}$. However, rolling 1 or 2 or 3 or 4 or 5 or 6 on fair die is individually NOT an eually likly event as the probability of occurrence of rolling 1 or 2 or 3 or 4 or 5 or 6 is $\frac{1}{6}$, whereas the probability of non-occurrence is $\frac{5}{6}$. $\underset{–}{\text{Remark:}}$ Two events are said to be equally likely or equi-probable events if their probabilities are equal to each other. Hence, rolling 1, 2, 3, 4, 5, 6 on a fair die are equally likely events or equi-probable events as their individual probability of occurrence is equal, and it is $\frac{1}{6}$.