Question

prove additive law of probability​

Answer 1

The addition rule for probabilities describes two formulas, one for the probability for either of two mutually exclusive events happening and the other for the probability of two non-mutually exclusive events happening. The first formula is just the sum of the probabilities of the two events.

Answer 2

ANSWER

Addition theorem of probability →

If A and B are any two events then the probability of happening of at least one of the events is defined as

P(A∪B)=P(A)+P(B)−P(A∩B)

Proof:-

From set theory, we know that,

n(A∪B)=n(A)+n(B)−n(A∩B)

Dividing the above equation by n(S) both sides we have,

n(A∪B)/n(s) = n(A)/n(s) + n(B)/n(s) − n(A∩B)/n(s)

P(A∪B)=P(A)+P(B)−P(A∩B)

(∵P(X)= n(X)/n(s)

Hence proved .