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The probability of shooting a target increases after a

by swerve » Wed May 09, 2018 12:42 pm

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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.

The OA is D.

Please, can anyone explain this PS question for me? I can't get the correct answer. I need help. Thanks.
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by Jay@ManhattanReview » Wed May 09, 2018 9:53 pm
swerve 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.

The OA is D.

Please, can anyone explain this PS question for me? I can't get the correct answer. I need help. Thanks.
Say,

The original probability of shooting the target = p;
The original probability of NOT shooting the target = q;

=> p + q = 1

=> The new probability of shooting the target = q; it is given that it is equal to the new probability of NOT shooting the target
=> Thus, the new probability of NOT shooting the target = p;

Since it is given that The probability of shooting a target increases after a certain skill is enhanced, p < 0.5 and q > 0.5 so that after the skill is enhanced, they swap their values.

We see the following deductions:

1. The original probability of shooting the target = p < 0.5;
2. The original probability of NOT shooting the target = q > 0.5;
3. The new probability of shooting the target = q > 0.5;
4. The new probability of NOT shooting the target = p < 0.5

Let' see each statement one by one.

A. The new probability of shooting the target is greater than 0.5.

See the deduction #3. It is rather correct, not false.

B. The original probability of shooting the target is less than 0.5.

See the deduction #1. It is rather correct, not false.

C. The original probability of NOT shooting the target and the new probability of shooting the target are the same.

See the deduction #2 and #3. It is rather correct, not false.

D. The original probability of shooting the target and that of NOT shooting the target are the same.

See the deduction #1; its value is p. See the deduction #2; its value is q. p ≠ q. This must be false. The correct answer.

E. The sum of the original and the new probabilities of shooting the target is ALWAYS equal to 1.

The original probability of shooting the target = p; and
The new probability of shooting the target = q

We know that p + q = 1. It is rather correct, not false.

The correct answer: D

Hope this helps!

-Jay
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Probability

by GMATGuruNY » Thu May 10, 2018 4:12 am
swerve 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.
Test an EASY CASE.
Let:
S = the original probability of shooting the target
NS = the original probability of NOT shooting the target
New S = the new probability of shooting the target
New NS = the new probability of NOT shooting the target

Case 1:
Let NEW NS = 0.1, implying that the NEW S = 0.9.
Since the original probability of shooting the target is equal to NEW NS, we get:
S = 0.1.
NS = 0.9.

The correct answer must be false in Case 1.

A. The new probability of shooting the target is greater than 0.5.
Since NEW S = 0.9, this option is TRUE in Case 1.
Eliminate A.

B. The original probability of shooting the target is less than 0.5.
Since S = 0.1, this option is TRUE in Case 1.
Eliminate B.

C. The original probability of NOT shooting the target and the new probability of shooting the target are the same.
Since NS = 0.9 and NEW S = 0.9, this option is TRUE in Case 1.
Eliminate C.

D. The original probability of shooting the target and that of NOT shooting the target are the same.
Since S = 10% and NS = 90%, this option is FALSE in Case 1.
Hold onto D.

E. The sum of the original and the new probabilities of shooting the target is equal to 1.
Since S = 0.1 and NEW S = 0.9, this option is TRUE in Case 1.
Eliminate E.

The correct answer is D.
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