The probability of shooting a target increases after a

In fact, the key formula here to solve the whole problem is:

\(P(A)=1-P(not\;A)\)

Then differentiate between the initial situation and the new (or final) situation:

Initial: \(P(A)=1-P(not\;A)\)

New: \(P(Z)=1-P(not\;Z)\)

And link the formulas with the conditions given by the problem.

1. Let p(i), q(i), be the initial probability of shooting and missing the target respectively and let p(n) and q(n) be the new probability of shooting and missing the target respectively.

Given:

1. p(i) + q(i) =1
2. P(n) + q(n) =1
3. p(n) > p(i)
4. p(i) = q(n)

Deductions:

5. q(n) + q(i) =1 ( from (1) and (4) )
6. p(n) + p(i) =1 ( from (2) and (4) ) - ( Choice E always true)

7. From ( 3) and (6), p(i) < 0.5 and p(n) > 0.5 - ( Choice A and Choice B always true)

8. From (1) and (6), q(i) = p(n) - ( Choice C always true)

9. From (3) and (8), q(i) > p(i) - ( choice D always false)

Therefore the answer is Choice D.

Sravna, what's the source of this question?

I find a little bit out of scope of GMAT

Thanks
Cheers
J

Can you specify the source of this question ? Further, is there an easier way to solve the question ? Listing out the nine cases is time consuming !

Original :
Let the probability of shooting the target be x. So, probability of not shooting the target will be 1-x
Similarly for new probability. Let the probability of shooting the target be y. So, probability of not shooting the target be 1-y
Now x = 1-y as per questiosn stem

So, x+ y = 1. SO y = 1-x

Original : P (Shooting) = x, P (not shooting) = 1-x
New : P (Shooting) = y = 1-x, P (not shooting) = 1-y = x.

Lets come to the option now.
A. The new probability of shooting the target is greater than 0.5. Yes it is true. Since new probability increase so, earlie it must be smaller than 0.5 and now it muct have increased above 0.5
B. The original probability of shooting the target is less than 0.5. Yes it is true due to same reason as described in A.
C. The original probability of NOT shooting the target i.e. 1-x and the new probability of shooting the target i.e. 1-x are the same. yes it is true.
D. The original probability of shooting the target and that of NOT shooting the target are the same. NO This is not true. original proabability of shooting the target is x andn NOT shooting the target is 1-x . both are not same.
E. The sum of the original and the new probabilities of shooting the target is ALWAYS equal to 1. x+ y = 1. Yes it is TRUE.

Answer D.
Though it took lots of time to figure it out.

A,B are correct
C is right because both the new and the original of NOT shooting are same
E is based on the same logic with C.

Can someone explain the following? If the skill is enhanced and is equal to the new probability of NOT shooting the target, then assuming A is correct the sum of both would be greater 1. So how can A be correct?

It should be equal to not greater than. Assuming its a binomial distribution.

Let original probability of shooting a target = a

ORIGINAL probability of NOT shooting the target = NEW probability of NOT shooting the target = b = NEW probability of shooting a target

=> a + b = 1