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# How to Determine wether A and B are Mutually Exclusive and Independent

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1. I've been given the information:
P(A) = 0.25 P(B) = 0.4 and P(A'nB') = 0.45

With this information how do I determine if A and B are Mutually Exclusive and/or Independent?
I've been given the information:
P(A) = 0.25 P(B) = 0.4 and P(A'nB' = 0.45

With this information how do I determine if A and B are Mutually Exclusive and/or Independent?
Use the Event Independence Test.

Two events are independent if, and only if, , and also follows from it.

3. (Original post by RDKGames)
Use the Event Independence Test.

Two events are independent if, and only if, , and also follows from it.

Is P(AnB) the same as 1- P(A'nB')?
Is P(AnB) the same as 1- P(A'nB'?
Yes. I think. Not the best at probability so I'm unsure.

Also if two events are mutually exclusive then (ie: the probability of A and B happening at the same time is 0)
Is P(AnB) the same as 1- P(A'nB'?
No. .
You need to find to see the events are independent.
6. As above, note that So

and can you take it from there?
7. In addition to what others have stated above, note De Morgan's Law:

(Source: http://www.math-only-math.com/proof-...rgans-law.html )

Find and use the formula for independence of two events and what it means if two events are mutally exclusive to each other.

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Updated: September 15, 2016
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