Is the Formula for the Probability of Symmetric Difference Accurate?

[GreenPrint]

Homework Statement

Show that the formula: P(AΔB) = P(A) + P(B) - 2P(A$\bigcap$B)

Homework Equations

The Attempt at a Solution

P(AΔB) = P(A) + P(B) - 2P(A$\bigcap$B)

P(AΔB) = P(A$\bigcap B^{c}$)$\bigcup (A^{c}\bigcap B)$

I don't know where to go from here. Thanks for any help.

 

[Mark44]

Homework Statement

Show that the formula: P(AΔB) = P(A) + P(B) - 2P(A$\bigcap$B)

Show that the formula does what?

Homework Equations

Definition of P(AΔB), perhaps?

The Attempt at a Solution

P(AΔB) = P(A) + P(B) - 2P(A$\bigcap$B)

P(AΔB) = P(A$\bigcap B^{c}$)$\bigcup (A^{c}\bigcap B)$

I don't know where to go from here. Thanks for any help.

 

[tiny-tim]

Hi GreenPrint!

Hint: how would you prove area(AΔB) = area(A) + area(B) - 2area(A$\bigcap$B) ?

 

[Ray Vickson]

Homework Statement

Show that the formula: P(AΔB) = P(A) + P(B) - 2P(A$\bigcap$B)

Homework Equations

The Attempt at a Solution

P(AΔB) = P(A) + P(B) - 2P(A$\bigcap$B)

P(AΔB) = P(A$\bigcap B^{c}$)$\bigcup (A^{c}\bigcap B)$

I don't know where to go from here. Thanks for any help.

Use Venn diagrams; that's their purpose.