How to add independent random variables?

Question

Probability theory

It's always hard for me and the dudes from work to get together and go out for a beer. Either someone has a repair, then a child, then something else. And today, when once again the trip to the tavern fell through, words were said about evil fate and "My wife meets with her friends even more often!".
I gave an explanation of our failures on the example of Alice and her 4 friends for each of whom the opportunity to go to the pub will fall with a probability of 50%. It turns out the probability that they will all come together is 6.25%.
Very similar to the truth.
But what if Alice doesn't care who to drink with, as long as she's not alone. And if for her random drinking companion the probability is 25%, then for her 25%. You might think that if there are two drinking companions, then already 50%. What if 4? 100%. Of course not. And then I realized that adding independent random variables is not easy. Only some incomprehensible formulas are googled, for me it is a dark forest.
Please explain on your fingers how to add independent random variables.

Answer 1

Alice has a probability to drink = 1 - (1 - probability_that_drinking buddy_will agree) ** (number of drinking buddies)
** - exponentiation
I.e. 1 - the probability that no one agrees.
For 4 drinking buddies = 1 - (1 -0.5)**4 = 1 - 0.625 = 0.9375