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 options:
A) 12 / 112
B) 6 / 81
C) 11 / 61
D) 12 / 33
E) 3 / 19

Rationale: "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 8 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 18 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 18 * 2 b * b 3 b - 2 b ^ 2 = 36 b ^ 2 3 b = 38 b ^ 2 b = 3 / 38 so , a = 2 b = 6 / 38 = 3 / 19 the correct answer is e ."
Answer: E