Question

Discuss the concepts of mutually exclusively events and independent events. List two examples of each type of events from everyday life.

Write in your own words in text not in text image since i cant read some of the handwriting in image

Answer 1

Mutually Exclusive Events

Two or more events are said to be mutually exclusive if the occurrence of 2 or more such events does not occur at the same time

Example: 1)In a 6 sided die events "2" and "3" are mutually exclusive because they can not occur at the same time when we throw one die. So the probability of occurrence at the same time will be zero.

i.e. P(A n B)=0

Example 2) Drawing of two kings in a suit of spade are mutually exclusive as in each of the suit(spade,club,diamond,hearts) there is only one king hence they are mutually exclusive.

Independent Events:

Two event A and B said to be independent if occurrence of A does not depend on the the occurrence of B.

Example 1): Winning of football match and raining today is said to be independent because wining of football match and raining today does not depend on each other.

Example 2): Passing percentage of student of university of Oxford and university of California are said to independent because their passing percentage does not depend on each other.

If two events A and B are independent then P(A n B)=P(A)*P(B)