How to calculate intersection and union of probabilities? lets say I have a switch A with 3 legs, each leg has 0.8 chance to be connected (and then electricity will flow), we need only 1 leg connected for A to transfer the electricity (so sorry I didn't explain it that well I'm having hard time to translate this problem)
So I calculated the chance of A to transfer electricity by doing $1-(0.2)^3$  which is $124\over125$ which I think is true.
The problem is I wanted to say that A will transfer elecricity only if 1 of his legs will be connected so its like saying $0.8 + 0.8 + 0.8$ which is obviously wrong(over $1$) so I used the weird formula that says to do like this: $0.8 + 0.8 + 0.8 - (0.8)^2 -(0.8)^2 - (0.8)^2 + (0.8)^3 = {124\over125}$ too.
My only problem is that I didnt understand why I had to use that formula and why I could multiple probabilities for the intersection but couldn't just sum them for the union.
Thanks in advance

Hint One of the three legs running isnt dependent on the running of other two legs. So the events are independent events. So we just multiply their probabilities instead of adding . 
