Answer the following questions based on probability rules:

(a) If Pr(A) = 0.3, Pr(B) = 0.5, and Pr(A B) = 0.6, what is Pr(A B)?

(b) If Pr(A B) = 0.2 and Pr(B) = 0.7, what is Pr(A|B)?

(c) If Pr(A) = 0.4, Pr(B) = 0.3, and Pr(AB) = 0.2, then are A and B independent?

(d) If Pr(B) = 0.8, Pr(A|B) = 0.6, and Pr(A|BC) = 0.5, what is Pr(B|A)?

(e) In a university, 30% of the students watch soccer and 40% of the students watch

basketball. Given that 20% of those that watch soccer also watch basketball,

what percent of those that watch basketball also watch soccer?

(f) One percent of population have a certain disease. For a medical test, 92% percent

of those who have the disease will get a positive result, and 8% of those who do

not have the disease will also get positive result (false positive). What is the

probability that a person has the disease given positive report?

(g) One bag (called Bag A) contains 6 white and 1 black balls while another bag

(called Bag B) contains 1 white and 6 black balls. One ball is drawn at random

from one of the bags, and it is found to be black. Find the probability that it

was drawn from Bag A.