Write the types of probability event.
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Answer:
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Step-by-step explanation:
Types of Events in Probability:
Some of the important probability events are:
Impossible and Sure Events
Simple Events
Compound Events
Independent and Dependent Events
Mutually Exclusive Events
Exhaustive Events
Complementary Events
Events Associated with “OR”
Events Associated with “AND”
Event E1 but not E2
Impossible and Sure Events
If the probability of occurrence of an event is 0, such an event is called an impossible event and if the probability of occurrence of an event is 1, it is called a sure event. In other words, the empty set ϕ is an impossible event and the sample space S is a sure event.
Simple Events
Any event consisting of a single point of the sample space is known as a simple event in probability. For example, if S = {56 , 78 , 96 , 54 , 89} and E = {78} then E is a simple event.
Compound Events
Contrary to the simple event, if any event consists of more than one single point of the sample space then such an event is called a compound event. Considering the same example again, if S = {56 ,78 ,96 ,54 ,89}, E1 = {56 ,54 }, E2 = {78 ,56 ,89 } then, E1 and E2 represent two compound events.
Independent Events and Dependent Events
If the occurrence of any event is completely unaffected by the occurrence of any other event, such events are known as an independent event in probability and the events which are affected by other events are known as dependent events.
Mutually Exclusive Events
If the occurrence of one event excludes the occurrence of another event, such events are mutually exclusive events i.e. two events don’t have any common point. For example, if S = {1 , 2 , 3 , 4 , 5 , 6} and E1, E2 are two events such that E1 consists of numbers less than 3 and E2 consists of numbers greater than 4.
So, E1 = {1,2} and E2 = {5,6} .
Then, E1 and E2 are mutually exclusive.
Exhaustive Events
A set of events is called exhaustive if all the events together consume the entire sample space.
Complementary Events
For any event E1 there exists another event E1‘ which represents the remaining elements of the sample space S.
E1 = S − E1‘
If a dice is rolled then the sample space S is given as S = {1 , 2 , 3 , 4 , 5 , 6 }. If event E1 represents all the outcomes which is greater than 4, then E1 = {5, 6} and E1‘ = {1, 2, 3, 4}.
Thus E1‘ is the complement of the event E1.
Similarly, the complement of E1, E2, E3……….En will be represented as E1‘, E2‘, E3‘……….En‘
Events Associated with “OR”
If two events E1 and E2 are associated with OR then it means that either E1 or E2 or both. The union symbol (∪) is used to represent OR in probability.
Thus, the event E1U E2 denotes E1 OR E2.
If we have mutually exhaustive events E1, E2, E3 ………En associated with sample space S then,
E1 U E2 U E3U ………En = S
Events Associated with “AND”
If two events E1 and E2 are associated with AND then it means the intersection of elements which is common to both the events. The intersection symbol (∩) is used to represent AND in probability.
Thus, the event E1 ∩ E2 denotes E1 and E2.
Event E1 but not E2
It represents the difference between both the events. Event E1 but not E2 represents all the outcomes which are present in E1 but not in E2. Thus, the event E1 but not E2 is represented as
E1, E2 = E1 – E2
Types of Events in Probability:
Some of the important probability events are:
Impossible and Sure Events
Simple Events
Compound Events
Independent and Dependent Events
Mutually Exclusive Events
Exhaustive Events
Complementary Events
Events Associated with “OR”
Events Associated with “AND”
Event E1 but not E2