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 3 times the probability that both events A and B occur. What is the probability that event A occurs?
Pick one
A) 44/7 B) 9/8 C) 25/8 D) 3/4 E) 7/8
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) = 3 times Probability (A and B)   a*(1-b) + b*(1-a) + ab = 3*ab   Substituting a=2b in the second equation:   2b*(1-b) + b*(1-2b) + 2b*b = 3*2b*b   3b-2b^2 = 6b^2   3b = 8b^2   b = 3/8 = 3/8   So, a = 2b = 3/4   THE CORRECT ANSWER IS 3/4.
<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 3 times the probability that both events A and B occur. What is the probability that event A occurs?