What is the probability that a field gun will hit thrice on

I think the wording of this question is not the one the realistic GMAT question would use, so I don't like this problem at all. Anyway:

What is the probability that a field gun will hit thrice on target in five tryouts?

If the probability of a certain event is \(p\), then the probability of it occurring \(k\) times in \(n\)-time sequence is: \(P = C^k_n*p^k*(1-p)^{n-k}\) (binomial distribution).

For our case we are asked to calculate \(P = C^3_5*p^3*(1-p)^{2}\). So all we need is the value of p.

(1) The field gun maintains a history of hitting once on target in every five tryouts --> p=1/5. Sufficient.

(2) The probability that the field gun will hit twice on target in five tryouts is 0.2048 --> \(P = C^2_5*p^2*(1-p)^{3}\) --> we'll get 3 values for p: one negative (not valid) and two positive (0.2 and ~0.63). Not sufficient.

Answer: A.

For more on this subject check Probability chapter of Math Book: math-probability-87244.html

Questions about the same concept to practice:
there-is-a-90-chance-that-a-registered-voter-in-burghtown-56812.html#p717422
in-how-many-different-ways-can-the-letters-a-a-b-91460.html

Hope it helps.