We know that Probability of an event E, written as
P(E)
$= \frac{N u m b e r o f o u t c o m e s f a v o u r a b l e t o E (m)}{N u m b e r o f a l l p o s s i b l e o u t c o m e s o f t h e e x p e r i m e n t (n)}$ .

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

m = n > 0

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m \geq 0, n > 0, m \leq n

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m \geq 0 \geq n

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0 \geq m \geq n

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Solution

The correct option is B $m \geq 0, n > 0, m \leq n$
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.
$H e n c e, P (E) = \frac{m}{n} \leq 1 \Rightarrow m \leq n$
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.
$\Rightarrow m \geq 0, n > 0, m \leq n$
Thus, the correct option is B.

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