Sandsynlighed

Jeg er i tvivl om det rigtige svar er b eller c, men jeg hælder mest til c?

Background
Calls for primary care providers (PCPs) to offer obese patients behavioral weight-loss counseling have not been accompanied by adequate guidance on how such care could be delivered. This randomized trial compared weight loss during a 2-year period in response to three lifestyle interventions (...).
Methods
We randomly assigned 390 obese adults in six primary care practices to one of three types of intervention: usual care (...); brief lifestyle counseling (...); or enhanced brief lifestyle counseling (...).
Results
(...)(T)he mean (±SE) weight loss with usual care, brief lifestyle counseling, and enhanced brief lifestyle counseling was 1.7±0.7, 2.9±0.7, and 4.6±0.7 kg, respectively. Initial weight decreased at least 5% in 21.5%, 26.0%, and 34.9% of the participants in the three groups, respectively. Enhanced lifestyle counseling was superior to usual care on both these measures of success (P=0.003 and P=0.02, respectively) (...).
Conclusions
Enhanced weight-loss counseling helps (...) obese patients achieve long-term, clinically meaningful weight loss.

What is the interpretation of the p-value of 0.003 in the above abstract?
a) The probability that enhanced lifestyle counseling was more effective than usual care is 0.003.
b) There is a 0.003 probability that enhanced lifestyle counseling reduces average weight by 4.6 kg when usual care reduces average weight by 1.7 kg.
c) If in reality there were no difference in weight reduction between usual care and enhanced lifestyle counseling, there would be a 0.003 probability that a random sample would should a difference of 4.6-1.7=2.9kg weight reduction.
d) Weight in the usual care group reduced by 1.7x0.003=0.0051 kg per day.