Sample
Space:

Definition:

In probability theory, the sample space of an trial or random experimental is the set of
all probable results or fallouts of that trial.

Explanation:

You decided to do a arbitrary test of rolling
a solo fair die with six edges. A accidental
trial is one where you cannot be sure what the result would be
prior to performing the trial. An result is a probable upshot of the trial.
Each side of the die has 1, 2, 3, 4, 5 or 6 marks. What are all the possible results
for this test? In a solo roll of the die, it can show 1, 2, 3, 4, 5 or 6 marks.
The complete list of possible outcomes for this trial is: 1, 2, 3, 4, 5, 6. The
set whose members are all probable outcome of a random test is called the sample space for that experiment.
For our die-rolling experiment, we can write the sample space as:

S =
{1, 2, 3, 4, 5, 6}

Example:

 A rotator
has 4 equal parts painted yellow, blue, green and red. What is the possibility
of landing stage on each color after rotating this rotator?

Sample Space: {yellow,
blue, green, red}

Probabilities:

P(yellow)

 = 

1

4

 

P(blue)

 = 

1

4

 

P(green)

 = 

1

4

 

P(red)

 = 

1

4

 

 

 

 What
is the likelihood of each result when a solo 6-sided die is rolled?

Sample Space: {1,
2, 3, 4, 5, 6}

Probabilities: 

P(1)

 = 

1

6

 

P(2)

 = 

1

6

 

P(3)

 = 

1

6

 

P(4)

 = 

1

6

 

P(5)

 = 

1

6

 

P(6)

 = 

1

6

 

 

 

 

 

 

 

 

 

 

 

Event:

Definition:

In probability theory, an event is a set of results of an experimentation (a subclass
of the sample space) to which a probability is
allotted.

Explanation:

There are many sorts of events for instance…

Simple event: Simple events are
the measures where one
test occurs at a time and it will be having a solo outcome.

It is represented by P(E) where E is the event

Joint
event: A joint probability
is a numerical measure
where the possibility of two events
happening together and at the same point in time are calculated. Joint probability is the likelihood
of occasion Y happening
at the same time event X
happens.

Compound
event:  A compound
event is one in which there is more than one probable upshot.

Example:

 Event: A card is nominated at arbitrary
from a typical deck of 52 playing cards. Without swapping it, a second card is selected.
What is the likelihood that the initial card elected is a queen and the next
card selected is a jack?

Probabilities:

P(queen on primary choice)

 = 

 4 

52

 

P(jack on 2nd choice assumed queen on 1st pick)

 = 

 4 

51

 

P(queen and jack)

 = 

 4 

 · 

 4 

 = 

  16  

 = 

  4  

52

51

2652

663

 

 

 

 

 

 

Venn Diagram:

Definition: A Venn
diagram is a figure that
shows all conceivable logical relations between a limited collection of
different sets.

History:  JV, was the discoverer of the
Venn diagram. He built the Venn diagram to support prove inclusion and
exclusion relationships among sets, except he did not sound it the ‘Venn
diagram.’ He named the rings ‘Eulerian circles.’

Explanation:

These figures depict elements as points in the plane, and sets as sections
inside closed curves. A Venn diagram consists of many overlapping closed arcs,
usually circles, each representing a set. The points inside a curve characterized S
represent elements of the set S, while points outside the border
represent elements not in the set S.

Example:

 

x

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