Statistic/Probability

Question

Suppose that P(A) = 1/5, P(B) = 4/5, and P(A or B ) = 1/3. Are A and B disjoint events? What is the value of 𝑃(𝐴|𝐵)?

Answer 1

Prob( A or B ) = Prob(A) + Prob(B) - Prob(A and B)

solves for Prob(A and B):

Prob(A and B) = Prob(A) + Prob(B) - Prob(A or B)

= 1/5 + 4/5 - 1/3 = 2/3

PRob(A | B) = Prob(A and B) / Prob(B) = 2/3 divided by 4/5 = 2/3 * 5/4 = 10/12 = 5/6