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 12 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 choices.
A) 21/26 B) 25/26 C) 11/26 D) 6/26 E) 22/33
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) = 12 times Probability (A and B)   a*(1-b) + b*(1-a) + ab = 12*ab   Substituting a=2b in the second equation:   2b*(1-b) + b*(1-2b) + 2b*b = 12*2b*b   3b-2b^2 = 24b^2   3b = 26b^2   b = 3/26 = 3/26   So, a = 2b = 6/26   THE CORRECT ANSWER IS 6/26.
<result>D</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 12 times the probability that both events A and B occur. What is the probability that event A occurs?