Show that the probability of the union of events A and B can be written as follows: 𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)[1 − 𝑃(𝐴/𝐵)] .

Question

Show that the probability of the union of events A and B can be written as follows:

𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)[1 − 𝑃(𝐴/𝐵)] .

Answer 1

P(A) + P(B)(1 - P(A|B)) = P(A) + P(B) - P(B)P(A|B) = P(A) + P(B) - P(A and B) = P(A or B)