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

Question

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.

Bunuel · Accepted Answer

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.

petrifiedbutstanding · Answer

Bunuel, can you suggest an alternate method to approach this problem?

EvaJager · Answer

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.

walker · Answer

It's definitely not a GMAT question. Even the first statement "The field gun maintains a history of hitting once on target in every five tryouts." doesn't define the probability of hitting the target with the gun. History can be just 5 shots or 5000 shots but you need infinite historical data to say that p=1/5.

teal · Answer

Probability of getting exactly k results out of n trails = nCk/2^n (isn't this problem the same as getting three heads in five coin flips)

Can't we use the above formula to calculate the prob. for k= 3 hits

5C3/2^5

Shouldn't this be the answer?

Bunuel · Answer

The probability of success is 1/5 not 1/2, thus your solution is not correct. Check here: what-is-the-probability-that-a-field-gun-will-hit-thrice-on-127334.html#p1042999 (also check the links provided there for better understanding of the concept).

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

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