# Linearity of expectation

I understand the algebraic proof of the linearity of expectation, but I cannot grasp the intuition, especially when the random variables are not independent. It is even counterintuitive as you cannot simply add the probabilities of dependent random variables, but it does not affect on the expected value.

Can anyone explain the intuition behind the algebraic formula? How to think about it?

• such argument gives an algebraic proof, but it doesn't explain the reason behind the property – guser Dec 4 '17 at 20:30
• This provides an intuitive explanation. – Remy Dec 4 '17 at 20:37