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: