Question

Match the following types of events to their probability.

• A. $1$
• B. $0<\text{P(E)}<1$
• C. $0$

Answer 1

We know that the probability of an event $E$ occurring is given by:

$\text{P(E)}$
$=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

Let the number total number of outcomes of a certain experiment $E$ be $n$.

Let $a$ be the number of favorable outcomes in experiment $E$.

In the case of certain events, all the outcomes that turn up are favorable.

Hence, $n=a$.

$\therefore \text{P(E)}=\frac{n}{n}=1$

The probability of certain events is $1$.

In the case of Impossible events, none of the outcomes that turn up are favorable outcomes.

Hence, $a=0$.

$\therefore \text{P(E)}=\frac{0}{n}=0$

The probability of impossible events is $0$.

In the case of Probable events, some but not all of the outcomes that turn up are favorable outcomes.

Hence, $0<a<n$.

$\therefore \text{P(E)}=\frac{a}{n}$

The probability of probable events is $0<\text{P(E)}<1$

Hence:

$0<P\left(\text{Probable Event}\right)<1$

$P\left(\text{Certain Event}\right)=1$

$P\left(\text{Improbable Event}\right)=0$