**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)=1Analysis 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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