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