The probability of shooting a target increases after a : GMAT Problem Solving (PS)
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# The probability of shooting a target increases after a

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Senior Manager
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The probability of shooting a target increases after a [#permalink]

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18 Mar 2013, 06:03
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Difficulty:

75% (hard)

Question Stats:

42% (02:20) correct 58% (01:16) wrong based on 120 sessions

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The probability of shooting a target increases after a certain skill is enhanced and is equal to the new probability of NOT shooting the target. Given this fact, which of the following must be false?

A. The new probability of shooting the target is greater than 0.5
B. The original probability of shooting the target is less than 0.5
C. The original probability of NOT shooting the target and the new probability of shooting the target are the same
D. The original probability of shooting the target and that of NOT shooting the target are the same.
E. The sum of the original and the new probabilities of shooting the target is ALWAYS equal to 1.
[Reveal] Spoiler: OA

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Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com

Classroom and Online Coaching

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Re: The probability of shooting a target increases after a [#permalink]

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20 Mar 2013, 02:12
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Quote:
The probability of shooting a target increases after a certain skill is enhanced and is equal to the new probability of NOT shooting the target. Given this fact, which of the following must be false?

I think this is a 700 problem.

If I understood well the question, we have:

• initial probability of shooting target: $$P(success\;initial)$$
• initial probability of not shooting the target: $$P(not\;success\;initial)$$
• new probability of shooting target: $$P(success\;final)$$
• new probability of not shooting the target: $$P(not\;success\;final)$$

Conditions given by problem:

(1) $$P(success\;initial)=1-P(not\;success\;initial)$$

(2) $$P(success\;final)=1-P(not\;success\;final)$$

(3) $$P(success\;initial)<P(success\;final)$$

(4) $$P(success\;initial)=P(not\;success\;final)$$

Therefore:

$$P(success\;final)=1-P(success\;initial)$$

then

$$P(success\;initial)<1-P(success\;initial)$$ ---> $$P(success\;initial)<0.5$$

Conclusions:

(5) $$P(success\;initial)<0.5$$

(6) $$P(success\;final)>0.5$$

(7) $$P(not\;success\;final)<0.5$$

(8) $$P(not\;success\;initial)>0.5$$

(9) $$P(success\;final)=1-P(not\;success\;final)$$ ---> $$P(success\;final)=1-P(success\;initial)$$ ---> $$P(success\;final)+P(success\;initial)=1$$

Analysis of different options:

A. The new probability of shooting the target is greater than 0.5: TRUE, look at (6)
B. The original probability of shooting the target is less than 0.5: TRUE, look at (5)
C. The original probability of NOT shooting the target and the new probability of shooting the target are the same: TRUE, look at (4)
D. The original probability of shooting the target and that of NOT shooting the target are the same: FALSE
E. The sum of the original and the new probabilities of shooting the target is ALWAYS equal to 1: : TRUE, look at (9)
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Re: The probability of shooting a target increases after a [#permalink]

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20 Mar 2013, 07:45
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.
Senior Manager
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Re: The probability of shooting a target increases after a [#permalink]

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24 Mar 2013, 18:07
SravnaTestPrep wrote:
The probability of shooting a target increases after a certain skill is enhanced and is equal to the new probability of NOT shooting the target. Given this fact, which of the following must be false?

A. The new probability of shooting the target is greater than 0.5
B. The original probability of shooting the target is less than 0.5
C. The original probability of NOT shooting the target and the new probability of shooting the target are the same
D. The original probability of shooting the target and that of NOT shooting the target are the same.
E. The sum of the original and the new probabilities of shooting the target is ALWAYS equal to 1.

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.
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Srinivasan Vaidyaraman
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Classroom and Online Coaching

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Re: The probability of shooting a target increases after a [#permalink]

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24 Mar 2014, 08:56
SravnaTestPrep wrote:
The probability of shooting a target increases after a certain skill is enhanced and is equal to the new probability of NOT shooting the target. Given this fact, which of the following must be false?

A. The new probability of shooting the target is greater than 0.5
B. The original probability of shooting the target is less than 0.5
C. The original probability of NOT shooting the target and the new probability of shooting the target are the same
D. The original probability of shooting the target and that of NOT shooting the target are the same.
E. The sum of the original and the new probabilities of shooting the target is ALWAYS equal to 1.

Sravna, what's the source of this question?

I find a little bit out of scope of GMAT

Thanks
Cheers
J
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Re: The probability of shooting a target increases after a [#permalink]

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20 May 2016, 07:05
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 !
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Re: The probability of shooting a target increases after a [#permalink]

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20 May 2016, 13:28
I always get these questions right, but I take a lot of time!!

I took 3:20 to answer this one. How can I improve this specific aspect??
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Re: The probability of shooting a target increases after a   [#permalink] 20 May 2016, 13:28
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