Question

Example of two exhaustive events in probability

Answer 1

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●Exhaustive events may or may not be equally likely and mutually exclusive. There is no any particular formula to find the exhaustive events, but sure we are able to tell that events are exhaustive or not after go through below examples.


1) Consider the experiment of throwing a fair die and the event of getting a number less than or equal to 6. Now this particular event is certain in spite of being a single event whenever the die is thrown and hence this single event is also exhaustive.


2) Consider the die throwing experiment. Let the events be getting a number which is multiple of 2 {2, 4, 6} and event of getting factors of 6 {1, 2, 3, 6} and event of getting a {5}. Clearly all these events together are exhaustive.

EXAMPLES:


1: A die is tossed, tell the following events are exhaustive or not.

1) X = Get prime number ; Y = Get multiple of 2 ; Z = Get 1.

2) X = Get prime numbers; Y = Get composite numbers; Z = Get 1.

3) X = an odd number; Y = an even number

Solution: 

1) X = Events of getting a prime number = {2, 5, 3}

Y = Events of getting a number that is a multiple of 2 = {4, 2, 6} and

Z = Getting one = {1} 

If we toss a coin two of the above mentioned events sure we get. So These are exhaustive together but not mutually exclusive.

2) 
X = Events of getting a prime number = {2, 5, 3}

Y = composite number = {4, 6} and

Z = getting one = {1} 

Above mentioned events are all together exhaustive and mutually exclusive too.


3) X = events of getting an odd number = {1, 3, 5} and 

Y = events of getting an even number = {2, 4, 6}

These are exhaustive as well as equally likely.