The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 18 times the probability that both events A and B occur. What is the probability that event A occurs? Choose the correct choice from the following answers:
A) 12/112	B) 6/81	C) 11/61	D) 12/33	E) 3/19
Let us say probability of A occuring is a.   Let us say probability of B occuring is b.   a = 2b   Probability (either A or B or both) = 8 times Probability (A and B)   a*(1-b) + b*(1-a) + ab = 18*ab   Substituting a=2b in the second equation:   2b*(1-b) + b*(1-2b) + 2b*b = 18*2b*b   3b-2b^2 = 36b^2   3b = 38b^2   b = 3/38   So, a = 2b = 6/38=3/19   TH3/19 CORR3/19CT ANSW3/19R IS 3/19.
<result>E</result>
The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 18 times the probability that both events A and B occur. What is the probability that event A occurs?