Exhaustive Events

Introduction to exhaustive events:

Random Experiment:

Random experiment is an experiment in which outcome is not known in advance. For example, if a uniform unbiased coin is tossed, then the outcome may be tail or head.

Exhaustive Events:

All possible outcome of an experiment is called exhaustive events or exhaustive cases. In tossing a coin, either the head or tail turns up. There is no other possibility and therefore these are the exhaustive events.Let us see concepts and sample problems for exhaustive events. Two or more events that have the property that their union equals the sample space is called exhaustive event.

Exhaustive events covers all the possible outcomes that is sample space of the problem.


Exhaustive events:


Exhaustive events:

If two or more events together form sample space S then these events are said to be exhaustive events. I

Example 1:

In an experiment of throwing the die find the chance of exhaustive events.

Solution:

" n " throwing a die,

The events of getting an odd number and the event of getting an even number together form the sample space.

A = {The events of getting an odd number} = {1,3,5}


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

A ? B = {1,2,3,4,5,6} = {S}

So, they are exhaustive events.

Example 2:

In an experiment of tossing three coins, consider the following events.

A : exactly one head appears,

B : exactly two heads appear

C : exactly three heads appear

D : atleast two tails appear

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

A = {HTT, THT, TTH}

B = {HHT, HTH, THH}

C = {HHH}

D = { TTH, THT, HTT, TTT}

The events A, B, C and D together form the sample space S.

That is, S = A ? B ? C ? D. Therefore A, B, C and D are called exhaustive events.


Exhaustive events:


Example 3:

In an experiment of tossing two coins, consider the following events.

A : exactly one head appears,

B : exactly two heads appear

C : exactly two tails appear

S = {HH, HT, TH, TT}

A = {HT, TH}

B = {HH}

C = {TT}

The events A, B and C together form the sample space S.

That is, S = A ? B ? C. Therefore A, B and C are called exhaustive events.

Example 4:

In an experiment of card game find the chance of exhaustive events.

Solution:

" n " getting a card,

The events of getting an diamond card,event of getting an heartine card,event of getting an spade,event of getting an club card together form the sample space (S).

Sample space(S) = 54.

A = {The events of getting an diamond card } = {13}

B = {The events of getting an heartine card }  = {13}

C = {The events of getting an club card }        = {13}

D = {The events of getting an spade card }     = {13}

A ? B ? C ? D = {54} = {S}

So, they are exhaustive events.