**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)