Problem Solving

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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