What is the probability that a field gun will hit thrice on target in five tryouts?
(1) The field gun maintains a history of hitting once on target in every five tryouts.
(2) The probability that the field gun will hit twice on target in five tryouts is 0.2048.
This cannot be a real GMAT test question. The probability of hitting twice the target in 5 tryouts is not complementary to the probability of hitting the target three times in 5 tryouts. From the equation presented by Bunuel, it follows that between 0 and 1, there are two solutions for p. Moreover, the method of proving/finding the roots of that equation, is beyond the scope of the GMAT.
I guess the author of the question meant a D answer, as it can be easily checked that 1/5 is a solution of the equation in (2), and the same as the probability in (1). But probably he/she didn't think further, that there might be another valid solution.
PhD in Applied Mathematics
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