I don’t quite get this. How does N(d2) represent the probability that the call option expires in the money? 1) if it is in the money on what basis can it be guessed whether it will be exercised or not 2) or does it mean the probability that S (share price) will be higher than X (exercise price)
Anyone?
If it expires in the money, we make the (admittedly farfetched) assumption that the option holder isn’t an imbecile: he (or she) will exercise it.
As for how N(d2) represents the probability that it expires in the money . . . that’s a topic for a class in partial differential equations. You might want to try this: take my word for it. 
That’s been my strategy so far.
Haha Apart from some being imbeciles, there could also be a possibility of some preferring to sell the options instead of exercising them.
More so in my part of the world, perhaps. We have one amongst the most active derivatives markets in equities but I haven’t met many who use options outside speculation.
Not at expiration . . .