The only way to have an average of 1 is to have successfully made every single shot that you attempt; so as long as there was at least one miss, you can't reach the exact number of 1. You can get arbitrarily close, though!
About the 5/2, yes, that's a good way to think of it! 5/2 is the reciprocal of 2/5, because the two of them multiply together to become 1.
The Daily Challenge Team