Basic Set has no exploration rules. Module B2 the PCs are kind of expected to go from square to square until they hit an interesting point (at least in the forests but that's half the map). I don't want to do that detail so I just did a hex grid of the area using HexTML



Each hex has one interesting bit. B2 has four encounter areas, Cave of the Unknown and Caves of Chaos so that's six and I've assigned them to the non-base hexes. For each day of exploring chance of finding the interesting bit in a hex is:

Terrain	Exploring	Modifiers	Random Encounter
Clear	1-4 in 6		1-2 in 6
Forest	1-2 in 6	+1 if elf/halfling	1-4 in 6
Hills	1-3 in 6	+1 if dwarf/halfling	1-3 in 6
Marsh	1-2 in 6		1-3 in 6
Mountains	1-2 in 6	+1 if dwarf	1-2 in 6

Other Modifiers:

Clear LOS = 1-4 (already calculated)
Restricted LOS: -1 (already calculated)
Restricted Movement: -1 (already calculated)

Bad Weather: -1
Travel to hex then exploring: -1

PCs being stealthy: -1 explore and random encounter
PCs split up into 2 sections: +1 explore and random encounter (encounter runs into 1 section)