# Thread: Proof of probability formula involving AuB

1. ## Proof of probability formula involving AuB

I am stuck in proving that if two events A and B are independent then :

P(AuB)=P(A)+P(A')P(B)

I am stuck with this question i know that if two events are independent then P(AnB)= P(A)P(B)

thanks

2. P(AUB)=P(A)+P(B)-P(AB)

use indep....

=P(A)+P(B)-P(A)P(B)

=P(A)+P(B)[1-P(A)]

=P(A)+P(B)P(A').

3. OK i think i have got the answer

P(AuB)=P(A)+P(B)-P(A)P(B)
P(AuB)=P(A)+P(B)(1-P(A)
P(AuB)=P(A)+P(B)P(A')