Question

If the probability of happening of an event is $\frac{m}{n}$. The probability of event not happening is:

• A. $m$
• B. $\frac{m}{n}$
• C. $\frac{n-m}{n}$
• D. $1$

Answer 1

The correct option is C

$\frac{n-m}{n}$

Given that:
$P\left(E\right)$= Probability of happening of an event =$\frac{m}{n}$
Then, P(E') = probability of event not happening = 1 - P(E)
[$\because$ P(E) and P(E') are complementary events]

$P\left(E^{\prime }\right)=1-\frac{m}{n}=\frac{n-m}{n}$
Thus, the correct option is C.