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 5 times the probability that both events A and B occur. What is the probability that event A occurs?	Pick one: A) 1/45 B) 1/2 C) 1/8 D) 2/3 E) 2/11
Let us say probability of A occuring is a.   Let us say probability of B occuring is b.   a = 2b   Probability (either A or 1/2 or both) = 5 times Probability (A and 1/2)   a*(1-b) + b*(1-a) + ab = 5*ab   Substituting a=2b in the second equation:   2b*(1-b) + b*(1-2b) + 2b*b = 5*2b*b   3b-2b^2 = 110b^2   3b = 12b^2   b = 3/12 = 1/4   So, a = 2b = 1/2
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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 5 times the probability that both events A and B occur. What is the probability that event A occurs?