Probability Concepts- Addition Rule & Multiplication Rule

Most of the students might be confused about where to use Addition rule and Multiplication rule in probability. This article will give you a clear insight on where to add and multiply the Probabilities.

A student solves the following two problems like below:

Problem: A boy is allowed to pick a random number among numbers from 1 to 999. What is the probability that the picked number is divisible by either 3 or 5, but not both?

First, let’s find out how many numbers are divisible by 3. It is simply (999/3=333).
So probability of the picked number divisible by 3=333/999=1/3
Second, Find out how many numbers divisible by 5. It is simply (999/5=199).
So probability of the picked number divisible by 5=199/999
The probability that the picked number is divisible by either 3 or 5, but not both= 1/3+199/999=532/999. ---------------Addition Principle

Problem: A coin and a dice are thrown simultaneously. What is the probability that he will get head & three simultaneously?

The probability of getting an head= ½
The probability of getting three=1/6
The probability of getting head and three=1/2 x 1/6= 1/12 ------------Multiplication Principle.

Let’s know why did he use addition principle in 1st problem and multiplication principle in 2nd problem?

The approach depends on the type of relationship of events:
Events Relationship-----------Principle to be used
Mutually Exclusive Events-----Addition principle
Independent Events------------Multiplication Principle

Mutually Exclusive: Let’s say A & B are two events and they are said to be mutually exclusive if B doesn’t occur when A occurs and vice versa.
Independent Event: Let’s say A & B are two events and they are said to be independent if outcome of an event A doesn’t affect the outcome of event B and vice versa.
As the first problem is a case of mutually exclusive events i.e. the Number which he picked is either divisible by 3 or 5 but not both, he used addition principle.
As the 2nd problem is a case of independent events i.e. a dice throw and a coin throw are the events which are independent of each other, he used multiplication principle.

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