If p is the probability the event occurs, 1-p is the probability it does not. So the probability it does not occur on three experiments is (1-p)^3, and Statement 1 gives us the equation
(1 - p)^3 = 0.512
and we can take cube roots on both sides, and then solve for p (no need to do that work in DS but since 512 = 8^3, the cube root of 512/1000 is 8/10, so you'd find 1-p = 0.8 and p = 0.2), so Statement 1 is sufficient.
For Statement 2, the probability the event occurs twice in two tries is p^2. For the event to occur exactly once, it either occurs on the first try and not on the second, which happens with a probability of (p)(1-p), or it does not occur on the first try and does on the second, which also happens with a probability of (1-p)(p). Adding the two cases, the chance the event happens exactly once is 2(p)(1-p). So the ratio Statement 2 discusses, the ratio of the probability of one success to the probability of two successes, is equal to 2(p)(1-p) to p^2, or, dividing by p, is equal to 2(1-p) to p. But that's exactly what Statement 2 tells us. So Statement 2 is telling us something we could have figured out without using Statement 2 at all, and Statement 2 tells us no new information whatsoever -- Statement 2 is true for every possible value of p. So the answer is A.
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