Non-overlapping events and independent events?

I am so confused and need some help with my math :(


Thank you so much!





Discuss the concepts of non-overlapping (mutually exclusive) events and independent events.





How are these two concepts different?





List two examples of each type of event from everyday life.

Non-overlapping events and independent events?
Mutually exclusive events are ones which can't happen at the same time.


Examples


miss bus, catch bus


play chess, go to sleep





Independent events are those where the outcome of one does not affect the other.


Examples


win at chess, win the lottery


eat cornflakes or toast for breakfast, miss the bus.
Reply:Think of it this way:





If two events are independent, knowing that one happens give no information at all about whether the other will happen. So if A and B are independent and P(A)=1/2 and P(B)=1/3, then the probability that B will happen if A has already happened is STILL P(B|A)=1/3. Here, P(B|A) is the probability that B happens when you already know that A has happened.





Mutually exclusive events are ones that cannot happen together. So, if A and B are mutually exclusive and A happens, then you definitely know that B does not happen. This means you got extra information about B given what happens with A. So, P(B|A)=0.





Remember: independent events give no information about each other. Mutually exclusive events do: you know they can't both happen.
Reply:Two mutually exclusive propositions are propositions that logically cannot both be true





Two events are said to be independent if the result of the second event is not affected by the result of the first event.