Interesting probability question I need help with...

Hi all, new to the forum so please excuse any newbie traits I might have..

I have a question I need help with as I'm sure I'm missing something..

The probability of result X happening is consistently 5%

So if there are 1,000 events in a day you'd expect around 50 X results I think

However, if I only randomly pick 100 from the 1,000 events in the day, then is the probability of finding result X still 5%, or 5 from 100?? or could the fact that I'm only picking 10% of the events in a day mean that the 50 expected X results from 1,000 could ALL be in the 900 I DON'T choose on the day??

each event is a separate entity and not related

I hope someone with more knowledge then me can help, this has been bugging me for a while now

all the best