SampleSpace:Definition:In probability theory, the sample space of an trial or random experimental is the set ofall probable results or fallouts of that trial.Explanation:You decided to do a arbitrary test of rollinga solo fair die with six edges. A accidentaltrial is one where you cannot be sure what the result would beprior 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 resultsfor 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. Theset 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 rotatorhas 4 equal parts painted yellow, blue, green and red. What is the possibilityof 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     Whatis 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 subclassof the sample space) to which a probability isallotted.Explanation:There are many sorts of events for instance…Simple event: Simple events arethe measures where onetest occurs at a time and it will be having a solo outcome.It is represented by P(E) where E is the eventJointevent: A joint probabilityis a numerical measurewhere the possibility of two eventshappening together and at the same point in time are calculated. Joint probability is the likelihoodof occasion Y happeningat the same time event Xhappens.

Compoundevent:  A compoundevent is one in which there is more than one probable upshot.Example: Event: A card is nominated at arbitraryfrom 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 nextcard 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 Venndiagram is a figure thatshows all conceivable logical relations between a limited collection ofdifferent sets.History:  JV, was the discoverer of theVenn diagram. He built the Venn diagram to support prove inclusion andexclusion relationships among sets, except he did not sound it the ‘Venndiagram.

‘ He named the rings ‘Eulerian circles.’Explanation:These figures depict elements as points in the plane, and sets as sectionsinside closed curves. A Venn diagram consists of many overlapping closed arcs,usually circles, each representing a set. The points inside a curve characterized Srepresent elements of the set S, while points outside the borderrepresent elements not in the set S.Example:  

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