Question

For two arbitrary events A and B. show that P(A+B)= P(A)+ P(B)-P(AB)​

Answer 1

Answer:

For arbitrary events A, B, we have

P(A∪B)=P(A)+P(B)−P(A∩B). ...(1)

Since probability of an event is a non-negative quantity, equation (1) gives

P(A)+P(B)−P(A∩B)≥0

or P(A)+P(B)≥P(A∩B)

or P(A∩B)≤P(A)+P(B).