Question

State and prove addition theorem of probability for 3 events

Answer 1

Answer:

The addition rule is a result used to determine the probability that event A or event B occurs or both occur.

The result is often written as follows, using set notation:

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

where:

P(A) = probability that event A occurs

P(B) = probability that event B occurs

P(A U B) = probability that event A or event B occurs

P(A int B) = probability that event A and event B both occur

Proof:

For mutually exclusive events, that is events which cannot occur together: P(A int B) = 0

The addition rule therefore reduces to

P(A U B)= P(A) + P(B)

For independent events, that is events which have no influence on each other:

P(A int B) = P(A).P(B)

The addition rule therefore reduces to

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