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)

Leave a Reply

Your email address will not be published. Required fields are marked *