If you count the episodes that start out as exploring but quickly become something else, you might (MIGHT) get 50%.
Most Star Treks are:
- Diplomatic missions/ situations
- Intrigue / Espionage
- Outright conflict
- Rescue Missions / Colony Support
- Holodeck Hyjinx
I also don't count the bogus 24th century "B-Stories" that went on in the background of the primary story.
With DS9 having nearly entire multiple seasons devoted to war and conflict, and ENT having at least one (and fair parts of another), I call BS on 50% being about exploring. TOS was probably the best about it, and it probably didn't even get to 50%.
I like the exploration stuff too, but I'm not binary/ absolute about it. Star Trek is a lot of different things. It's never ever been one thing.
I count colony rescue and holodeck stories as exploration. DS9 fell well below 50%, ENT had a season that was almost 10% but overall Star Trek is above 50%