Question

We know that Probability of an event E, written as
P(E)
$=\frac{\text{Number of outcomes favourable to E(m)}}{\text{Number of all possible outcomes of the experiment (n)}}$.

Which of the following options correctly explains the relationship between m and n?

• A. $m=n>0$
• B. $m\ge 0,n>0,m\le n$
• C. $m\ge 0\ge n$
• D. $0\ge m\ge n$

Answer 1

The correct option is B

$m\ge 0,n>0,m\le n$

Following two points are worth noticing while checking the relationship between m and n:
1. The probability of occurring of an event can never be more than one.
$Hence,P\left(E\right)=\frac{m}{n}\le 1\Rightarrow m\le n$
And, 2. The number of events and the number of possible outcomes can never be negative. Thus, the value of m and n is always greater than 0.
$\Rightarrow m\ge 0,n>0,m\le n$
Thus, the correct option is B.