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?
Choose the correct choice from the following choices
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) &gt; 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) &lt; 0.5 and p(n) &gt; 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) &gt; p(i) - ( choice The original probability of shooting the target and that of NOT shooting the target are the same. always false)   Therefore the answer is Choice The original probability of shooting the target and that of NOT shooting the target are the same.
<result>D</result>
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?