Total Number of Events

Total number of events that occurs in a sample space is known as total number of events. It is the sum of all the simple and compound events. Total number of events can be found by;

Total Number of Events Formula

Total number of events = 2ⁿ

Where;

n = the number of things under observation. For example two coins, two dice etc…

Total Number of Events Examples:

1. Statement: Two coins are tossed. Write down the total number of events and the end also writes its sample space.

        Solution:

Total number of events = 2² = 4

These four events are;

• Head appears on both coins (H₁H₂) = E₁ = {(H₁H₂) }
• Head on first coin and tail on 2^nd coin (H₁T₂) = E₂= {(H₁T₂) }
• Tail on first coin and head on 2^nd coin (T₁H₂) = E₃ = {(T₁H₂)}
• Tail appears on both coins (T₁T₂) = E₄ = {(T₁T₂) }

Sample space = S = {(H₁H₂), (H₁T₂), (T₁H₂), (T₁T₂)}

1. Statement: A dice is thrown. Now write down all the events and also form a sample space.

     Solution:

When a dice is rolled then there are six “6” possible outcomes. Therefore, we can say it consists of     six events.

These events are;

• E₁ = {(1)}
• E₂ = {(2)}
• E₃ = {(3)}
• E₄ = {(4)}
• E₅ = {(5)}
• E₆ = {(6)}

So, sample space will be;

    Sample space = {1, 2, 3, 4, 5, 6}