If I roll a pair of dice, perhaps I will get the same number on both dice, but I probably will get different numbers. The weather tomorrow will probably be nice, but perhaps it will rain. I'll bring my umbrella just in case. PROBABLY means you expect something to happen. It means "likely," "almost certain." PERHAPS literally means "by chance" or "by luck." The event is unlikely, but possible--and if it does happen, we will say "Oh, what good luck" or "Oh, what bad luck." PERHAPS can also suggest an action we can take to protect ourselves against bad luck: "The weather tomorrow will probably be nice, but there's a 10% chances of rain, so perhaps I should bring my umbrella."

"Probably" is used when you are pretty sure of something, but not 100% certain (the most likely reason for something happening). "Perhaps" also conveys some doubt, but is used to just make suggestions. Here's an example: Rose: "Sam is late! He probably fell asleep again after he got home." Lewis: "Perhaps he is just stuck in traffic."

i would say that 'probably' is a 90% chance of something happening, while 'perhaps' is more of a 50% chance of something happening.