Fundamental Principle of Addition


 
 
Concept Explanation
 

Fundamental Principle of Addition

To find the total, number of ways in which either of the two jobs can be performed  when both the jobs are mutually exclusive jobs the fundamental principle is followed. If  the two jobs can be performed independently in  m and n ways respectively, then either of the two jobs can be performed in ( m+ n) ways.

In case of two events X and Y.  n(X) denotes the possible ways in which the event X can occurs n(Y) denotes the possible ways in which the event Y can occurs

Let Z be an event describing the situation in which either event X occurs, OR event Y occurs. Then, if n(Z) denotes the number of ways in which the event Z can occur or the number of possible outcomes of the event Z . It can be calculated using the Fundamental Principle of Addition and  is given by:

n(Z) = n(X) + n(Y)

For example: To calculate the total number of possible outcomes when either a coin is tossed or a dice is thrown the Fundamental Principle of Addition can be used as follows

Job 1: When a dice is thrown the possible outcomes are n(dice)= 6

Job 2: When a coin is tossed the possible outcomes are n(coin)= 2

The total number of possible outcomes when either a coin is tossed or a dice is thrown can be calculated as

n(dice or coin) = n(dice) + n(coin) =6 + 2= 8

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Sample Questions
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Question : 1

There are 5 Mathematics books and 6 Physics books in  a book shop. In how many ways a student can buy a mathematics book or a physics book?

Right Option : C
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Question : 2

There are 8 toy cars and 5 dolls in a shop. In how many ways the shopkeeper will either sell a toy car or a doll?

Right Option : A
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Question : 3

Which of the following statement is/are  correct?

(a) In a class there are 4 boys  and 3 girls. Teacher wants to select a boy or a girl . Teacher can make selection in 12 ways.

(b) In a shop there are 5 candies and 5 chocolates. A child wants to have a candy or a chocolate. A child can have a candy or a chocolate in 25 ways.

Right Option : D
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