Student: Seema Singh

Q. What are mutually exclusive and independent events? Can you explain with examples.


Answer :

Hi Seema,
In context of probability theory, there are various type of events which are classified into different categories. Taking a 
daily life examples, outcome of tossing a coin, rolling a dice.
Two of most talked about events are Mutually exclusive event and Independent events.

Topic: Probability

Concept:
Mutually exclusive event : In simple terms it means occurrence of one of the events excludes the occurrence of the other.

Independent events : It means occurrence or non-occurrence of one  event does not influence the occurrence or non-occurrence of the other.

Explanation:
Mutually exclusive event : In simple terms it means occurrence of one of the events excludes the occurrence of the other. 
For example when a coin is tossed, you will get either Head or Tail. You can not get both Head and Tail simultaneously. Hence occurrence of Head and Tail are mutually exclusive events.
Independent events : It means occurrence or non-occurrence of one  event does not influence the occurrence or non-occurrence of the other.
For example When a coin is tossed two times, the event of getting Tail in the first toss and the event of getting Tail in the 
second toss are independent events. This is because the occurrence of getting Tail in any toss does not influence the occurrence of getting Tail in the other toss.

Examples:
Examples of Mutually exclusive events : 

  1. Tossing a coin: Heads and Tails are Mutually Exclusive.
  2. Turning left and turning right are Mutually Exclusive (you can`t do both simultaneously.

Examples of Independent events :

  1. Say you rolled a die and flipped a coin. The probability of getting any number face on the die in no way influences the probability of getting a head or a tail on the coin.
  2. The probability of rain today and the probability of my playing chess today are independent events as chess will be played,rain or shine.

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