Question

if a b c are three events associated with random experiment proved that p a union b union c is equals to be a + b + c c minus b intersection b minus b intersection C minus b a b intersection C plus b a union intersection b intersection c

Answer 1

Hey there!

Let's prove the above using Venn diagram.

The first attachment shows :- P(A) + P(B)+P(C) -
P( A ∩ B) - P( B ∩ C) - P ( A ∩ C) .

In the Venn diagram represents ,
Yellow represents P(A) .
Green represents P( B)
Blue represents P(C )

White represents -P( A ∩ B) - P( B ∩ C) - P ( A ∩ C) .

The second attachment shows, P(A) + P(B)+P(C) - P( A ∩ B) - P( B ∩ C) - P ( A ∩ C) + P ( A ∩ B ∩C)

The third attachments shows, The Venn diagram of P ( A ∪ B ∪ C) .

Here,
P ( A ∩ B ∩C) is represented by Brown.

P ( A ∪ B ∪ C) is represented by Violet.
By observations, We observe that Area of the second Venn diagram = Area of third Venn diagram.

Hence, We can conclude that P ( A ∪ B ∪ C) = P(A) + P(B)+P(C) - P( A ∩ B) - P( B ∩ C) - P ( A ∩ C) + P ( A ∩ B ∩C) .

There are 3 attachments. See all of them. View the answer in your browser or kindly visit this page :-
https://brainly.in/question/2810671