Random Event

Random event is an important concept that deals with the process of determining the possible outcomes of that event by using probability. However the outcomes are mostly unpredictable at the beginning and we can never have an exact value of the event. It is an important concept in probability.

What is Random Event in Probability?

We understand the concept of probability along with random events in probability.

Random Event Definition

A random event is an event that can not be predicted or is unpredictable at the beginning of an experiment. If a random event repeats in same number of times, it can still give different outcomes. In a random experiment, all the possible results are known in advance but none of them can be predicted with certainty. Tossing a coin is a random experiment as it is unpredictable and both heads and tails have 50% probability.

Now, a random event in probability means the application of probability in the determination of a possible number of outcomes of a random event. The examples of dice & coin toss are the two most important examples of random events, where the results are known but can not be predicted at the beginning. We will understand the topic with some examples in the next paragraph.

Probability Definition

Probability is the measure of the possible outcomes of an event. It is defined as a number between 0 and 1 (0 denoting improbability and 1 denoting certainty). It is a branch of mathematics that deals with the interpretation of random events.

For example:

When we toss a coin, either we get a head or a tail. Therefore only two outcomes are possible, i.e., (H, T). It can be expressed as:

P(X) = (Number of Favorable Ways in which X can happen)/ (Total Number of Ways in which Event Can Happen)

where,

P(X) is Possibility of Event X

This, is also explained using the formula:

P(X) = n/N

where,

n is Number of Favorable Outcomes
N is Number of Total Outcomes in a Random Event

Probability of a Random Event

To find the probability of a random events follow the steps added below:

For example, we toss an unbiased coin three times what is probability of getting three heads one after another. The sample space for the same is added below:

Step 1: Find sample space of random events: {(HHH), (HHT), (HTH), (HTT), (THH), (THT), (TTH), (TTT)}
Step 2: Find the number of events in the sample space (here, N = 8)
Step 3: Find the sample space of required event: {(HHH)}. Also, find the number of event in the sample space. (here, n = 1)
Step 4: Use the probability formula: P(X) = n/N,
Here,
P(Three Heads) = 1/8 = 0.125 = 12.5%

Examples on Random Event in Probability

Example 1: If 60% of Americans are not obese. What is the probability that a randomly selected group of 3 people will be obese?

Solution:

60% of Americans are not obese
So, 40% of Americans are obese
Also, 40% = 0.4
Possible ways in which random 3 people are obese, then:
P(X)=0.4×0.4×0.4
P(X)=0.064=6.4%
This is the process of finding the probability of a random event.

Example 2: Find the probability that a given day chosen in a week is Sunday.

Soultion:

There are a total 7 possible days in a week.
Possibility of Sunday = 1/7 = 0.142857143
= 14.29% (approx)
Thus, there is 14.29% chance that a random day chosen in a week is Sunday.

Example 3: One integer is chosen from 1, 2, 3, …... 100. What is the possibility that it is neither divisible by 4 nor divisible by 6?