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 8 times the probability that both events A and B occur. What is the probability that event A occurs? Choose the most appropriate option
A) 1/12	B) 1/8	C) 1/6	D) 1/3	E) 2/3
Let us say probability of A occurring is a.   Let us say probability of B occurring is b.   a = 2b   Probability (either A or B or both) = 8 times Probability (A and B)   a*(1-b) + b*(1-a) + ab = 8*ab   Substituting a=2b in the second equation:   2b*(1-b) + b*(1-2b) + 2b*b = 8*2b*b   3b-2b^2 = 16b^2   3b = 18b^2   b = 3/18 = 1/6   So, a = 2b = 1/3   ANSWER:1/3
<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 8 times the probability that both events A and B occur. What is the probability that event A occurs?