What is a simple event in probability? What is a complementary event?

Answer 1

See explanation.

A elementary event is (exactly speaking) a primary oobject which is not defined (as for example a point or a number).

More generally it is a "basic result" of a probability experiment. For example if a die is thrown the possible results (i.e. elementary events) are #1,2,3,4,5# and #6#
A set of all elementary events is called a sample space and denoted by #Omega#
An event is any subset of #Omega#
A complementary event of #A# is a set:
#A'={omega in Omega:omega !in A}#
so the complementary event consists of all elementary events which are not in the event #A#

Example

I wrote earlier about an experiment of a die throw. Its sample space is (as I wrote) a set of numbers #1#-#6#
#Omega = {1,2,3,4,5,6}#
Let #A# be an event a prime number is thrown.
Then #A={2,3,5}#, because in the set #Omega# only #2,3# and #5# are prime numbers
A complementary event would be #A'# - a number which is not prime is thrown, so
#A'={1,4,6}#
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Answer 2

A simple event in probability refers to an outcome or event that cannot be further broken down into simpler events. It is the most basic unit of probability analysis.

A complementary event in probability is the event that consists of all outcomes that are not part of the given event. In other words, if ( A ) is an event, then the complementary event of ( A ) is denoted by ( A' ) or ( A^c ), and it includes all outcomes that are not in ( A ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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