P. B. Sreenivas was born on September 22, 1930.

P. B. Sreenivas was born on September 22, 1930.

P. B. Sreenivas is 80 years old (birthdate: September 22, 1930).

if P(A)>0 then P(B'|A)=1-P(B|A)

so P(A intersect B')=P(A)P(B'|A)=P(A)[1-P(B|A)]

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

=P(A)P(B')

the definition of independent events is if P(A intersect B')=P(A)P(B')

that is the proof

Sum Rule:

P(A) = \sum_{B} P(A,B)

Product Rule:

P(A , B) = P(A) P(B|A) or P(A, B)=P(B) P(A|B)

[P(A|B) means probability of A given that B has occurred]

P(A, B) = P(A) P(B) , if A and B are independent events.