What are Simple and Compound Events in Probability?

Probability denotes how likely an event will happen. In probability, simple, compound and complementary events are different types of probabilities. These are calculated in a slightly different manner. As far as the JEE exam is concerned, probability is an important topic. In this article, we will learn what are simple and compound events probability .

Simple Event

An event that has a single point of the sample space is known as a simple event in probability.

For example, the probability of getting a 3 when a die is tossed.

Here S = { 1, 2, 3, 4, 5, 6}

If E be the event of getting a 3 when a die is tossed. E = { 3 }

P(E) = 1/6

In the case of a simple event, the numerator (number of favourable outcomes) will be 1.

Compound Event

If an event has more than one sample point, it is termed as a compound event. The compound events are a little more complex than simple events. These events involve the probability of more than one event occurring together. The total probability of all the outcomes of a compound event is equal to 1.

To calculate probability, the following formual is used:

Probability of an event = [The number of favourable outcomes] / [the number of total outcomes].

First, we find the probability of each event occurring. Then we will multiply these probabilities together. In the case of a compound event, the numerator (number of favourable outcomes) will be greater than 1.

For example, the probability of rolling an even number on a die, then tossing a head on a coin.

Here P(even number) = 3/6

P(head) = 1/2

Hence required probability = (3/6)(½ )

= 3/12

Also Read: Compound Probability

Solved Examples

Example 1:  A coin is thrown 3 times. What is the probability that atleast one head is obtained?

Solution: 

Sample space = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}

Total number of outcomes = 2 × 2 × 2 = 8.  

Favourable outcomes = 7

Required probability = 7/8

Example 2: What is the probability that a dice with 12 faces returns a value 9 if each face has a number starting from 0.

(A) 0                

(B) 1              

(C) 1/6               

(D) 1/12

Solution:

Total number of outcomes = 12

Favourable outcome = 1

Required probability = 1/12.

Hence option D is the answer.

Practice Problems

1. Find the probability of drawing a spade, replacing the card, then drawing a club.
2. What is the probability of rolling either a two or a four using one-sided die?

Answer key:

1. 169/2704

2.  1/5