So in the end the exactly didn't matter and I guessed this was why after this:

Pr (3 block) = 1 - (Pr( ≤2 block) + Pr (>3 block))
I still got the same 0.06133 which is roughly same as the 0.06131
But you're calculating exactly three in here. If P(block=3) = 1 - {every other possibility than P(block=3)), then you're calculating for exactly three. If you wanted to calculate for at least three, you would work out P(block >= 3), which is just 1 - P(block = 0) - P(block = 1) - P(block = 2) = 0.080302 ~= 8%.
 

Question: What is the chance of having exactly three blocks mined within the next 10 minutes? You can assume that a new block is mined every 10 minutes on average.

Another fun fact. The probability of not finding any block for 10 minutes is the same as finding exactly one block; about 36.8%.

That will be a little difficult. Block times are not accurate, as rightly said. Your best source of information is debug.log (in which it is written when your node received the blocks). But it won't be accurate either, because hashrate does not remain constant for a long time.