C is the event that exactly one of A and B occurs. You only need circles for A and B on the Venn Diagram
So it means that either:
A occurs (but not B)
or
B occurs (but not A)
So P(C) = P( n ) U P( n )
Can anyone tell me if this is the right Venn Diagram for denoting C the event that exactly one of A and B occurs?
Its the one on the right at this website:
Venn Diagram -- from Wolfram MathWorld
Also how would you write an expression for C in terms of unions, intersections and complement of A and B.
And then use that to find an expression of P(C) in terms of P(A),P(B) and P(A n B)
So P(C) = P( n ) U P( n )[/QUOTE] would be the expression for C in terms of unions, intersections and complements of A and B.
How would I use this to derive an expression for P(C) in terms of P(A), P(B) and P(AnB).
Would it be like this?
P(C) = ( P(A) - P(A n B) ) u ( P(B) - P(A n B))
This is the question:
(a) draw a Venn diagram
(b) Write down an expression for C in terms of union, intersections and complement of A and B.
(c) Using result (b) derive an expression for P(C) in terms of P(A), P(B) and P(A nB). Give a detailed proof of the result.
I dont no what the difference for the expression of C and the expression of P(C) is?