Question

Define independent and mutually exclusive events mathematically by using P(A) & P(B) for events A & B

Answer 1

"independent events" means they are independent of each other

P(A or B) = P(A)+P(B) - P(A and B)
and
mutually exclusive events" means they are complements of each other, either A or B happens
so P(A or B)=P(A)+P(B)
and P(A and B)=0

Answer 2

for independent events P(A and B)=P(A)*P(B)

Answer 3

if A & B are independent
then P(A/B) =P(A)
that is
P(A/B) =P(A & B)/P(B) [ probability of occurence of A when B ahs already occurred]

P(A/B) =P(A)
P(A & B)/P(B) = P(A)
hence condition for independent event
is
P(A & B) = P(B) * P(A)