
Probability question
Hey, lets say I have 5 probabilities of the chance that 5 different things are is "on", so the probabilities for each of the items would be something like:
.75, .81, .63, .9, .1
I'd like to calculate the probability that, given the individual probabilities, that 3 or more of these items are really "on".
I'm guessing the probability that all 5 are "on" is simply the 5 numbers multiplied together, which is ~.03.
I'd imagine I'd have to add this number to the probability that 4 are and on the probability that 3 of them are on to get the total probability for all possible outcomes? Not sure how to calculate these though...


Thanks for your reply. Ok so that's it then, I guess I posted it cause I thought there might be an easier way to calculate this, some kind of mathematical tool to do the job easily, unfortunately that doesn't seem to be the case, thanks again!
P

Just a comment on Soroban's solution
This solution assumes the events are independent. There is nothing in the problem statement to this effect. If it is *not* the case that the events are independent, then you do not have sufficient information to solve the problem.