Simple Events Examples

Events which cannot be disintegrated further are known as simple events. It is an event which cannot be broken down any further and has single outcome. The probability of simple event is number of favorable outcomes to total number of outcomes. For example, an event $\{Red,\ Blue,\ Green\}$ is not a simple event but an event $\{Red\}$ is a simple event.

Word problems

Let us see some examples to understand the concept better.
Problem 1:

There are $2$ green and $5$ black marbles. If one marble is chosen at random then what is the probability of getting green marble.

Solution:

The probability can be calculated by number of favorable events to total number of events.

Number of favorable events, $n(E)$ = $2$

Total events in sample space, $n(S)$ = $2\ +\ 5$ = $7$

Probability = $\frac{n(E)}{n(S)}$ = $\frac{2}{7}$
Problem 2:

Disintegrate the event of getting an odd number in a dice throw in simple events.

Solution:

The sample space of throwing a dice is $\{1,\ 2,\ 3,\ 4,\ 5,\ 6\}$.

The event of getting an odd number = $\{1,\ 3,\ 5\}$

This is the combination of events $\{1\}$, $\{3\}$, and $\{5\}$.

Hence, the simple events in which this event can be disintegrated is,

Event of getting a $1$.

Event of getting a $3$.

Event of getting a $5$.
Problem 3:

Two coins are tossed simultaneously. Which one of the following is a simple event?

a) Getting at least one tail.

b) Getting first head and then tail.

Solution:

The sample space for tossing two coins is $\{HH,\ HT,\ TH,\ TT\}$.

The event having at least one tail = $\{HT,\ TH,\ TT\}$

This can be disintegrated to $\{HT\},\ \{TH\},$ and $\{TT\}$. Hence, it is not a simple event.

The event of getting head first and then tail = $\{HT\}$. This is a simple event.
Problem 4:

Classify the given events.

a) The fan is on.

b) The fan is off.

Solution:

Both these events are simple events.

The fan cannot be on and off at same time, hence they are mutually exclusive simple events.

The probability of fan is on and fan is off sums up to $1$. Hence, they are complementary simple events.