A ball is drawn at random from a box containing 10 balls numbered sequentially from 1 to 10. Let X be the number of the ball selected, let R be the event that X is an even number, let S be the event that , and let T be the event that . Which of the pairs (R,S), (R,T), and (S,T) are independent?
I can solve this mathematically as such:
So is independent.
My question is, intuitively, how is independent, but not? Maybe I'm not understanding what to events being independent entails.