Deprecated: Function create_function() is deprecated in /home/techwond/public_html/wp-content/themes/spike/functions/widget-tabs2.php on line 433

Deprecated: Function create_function() is deprecated in /home/techwond/public_html/wp-content/themes/spike/functions/widget-recentposts.php on line 171

Deprecated: Function create_function() is deprecated in /home/techwond/public_html/wp-content/themes/spike/functions/widget-relatedposts.php on line 179

Deprecated: Function create_function() is deprecated in /home/techwond/public_html/wp-content/themes/spike/functions/widget-authorposts.php on line 176

Deprecated: Function create_function() is deprecated in /home/techwond/public_html/wp-content/themes/spike/functions/widget-popular.php on line 195

Deprecated: Function create_function() is deprecated in /home/techwond/public_html/wp-content/themes/spike/functions/widget-catposts.php on line 187
Proof of Addition Theorem on Probability Through Axiomatic Approach

# Proof of Addition Theorem on Probability Through Axiomatic Approach

According to Addition Theorem on Probability, for any two elements A, B

P(A∪B) = P(A) + P(B) – P(A∩B)

#### Addition Theorem on Probability Proof :-

Expressing A∪B as the union of two mutually exclusive events we get
(A∪B) = A ∪ (B-A)
P(A∪B) = P(A ∪ (B-A))
By applying axiom of union we get,
P(A∪B) = P(A) + P(B-A) since A, B-A are exclusive
= P(A) + P(B – (A∩B))
= P(A) + P(B) – P(A∩B) since P(B-A) = P(B) – P(A) when every A⊆B

note: If you find any errors then do correct in comment section below.
Therefore P(A∪B) = P(A) + P(B) – P(A∩B)