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Mutually Exclusive Events and Non-Mutually Exclusive Events
Mutually Exclusive Events and Non-Mutually Exclusive Events
9.3
Mutually Exclusive Events and Non-Mutually Exclusive Events
Mutually Exclusive Events and Non-Mutually Exclusive Events
A combined event
\(A\)
and
\(B\)
is known as a mutually exclusive event if there is no intersection between events
\(A\)
and
\(B\)
,
\(A \cap B \neq \emptyset\)
.
Verify the Formula of Probability of Combined Events for Mutually Exclusive and Non-Mutually Exclusive Events
Formula
The
combined event
\(A\)
and
\(B\)
is
non-mutually exclusive
because
\(P(A \cap B) \neq 0\)
,
\(P(A \space \text{or} \space B) = P(A) + P(B) - P( A\cap B)\)
.
The combined event
\(A\)
and
\(B\)
is
non-mutually exclusive
because
\(P(A \cap C) \neq 0\)
and
\(P(B\cap C) =0\)
, then
\(P(A \space \text{or} \space C) = P(A) + P(C) \space \text{and} \space P(B \space \text{or} \space C)= P(B) + P(C)\)
.
Addition Rule of Probability
\(P(A \cup B) = P(A) + P(B) \)
or
\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
Mutually Exclusive Events and Non-Mutually Exclusive Events
9.3
Mutually Exclusive Events and Non-Mutually Exclusive Events
Mutually Exclusive Events and Non-Mutually Exclusive Events
A combined event
\(A\)
and
\(B\)
is known as a mutually exclusive event if there is no intersection between events
\(A\)
and
\(B\)
,
\(A \cap B \neq \emptyset\)
.
Verify the Formula of Probability of Combined Events for Mutually Exclusive and Non-Mutually Exclusive Events
Formula
The
combined event
\(A\)
and
\(B\)
is
non-mutually exclusive
because
\(P(A \cap B) \neq 0\)
,
\(P(A \space \text{or} \space B) = P(A) + P(B) - P( A\cap B)\)
.
The combined event
\(A\)
and
\(B\)
is
non-mutually exclusive
because
\(P(A \cap C) \neq 0\)
and
\(P(B\cap C) =0\)
, then
\(P(A \space \text{or} \space C) = P(A) + P(C) \space \text{and} \space P(B \space \text{or} \space C)= P(B) + P(C)\)
.
Addition Rule of Probability
\(P(A \cup B) = P(A) + P(B) \)
or
\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
Chapter : Probability of Combined Events
Topic : Mutually Exclusive Events and Non-Mutually Exclusive Events
Form 4
Mathematics
View all notes for Mathematics Form 4
Related notes
Combined Events
Dependent Events and Independent Events
Quadratic Functions and Equations in One Variable
Number Bases
Statements
Arguments
Intersection of Sets
Union of Sets
Combined Operations on Sets
Chapter 5: Network in Graph Theory
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