Here is part of the solution . . .
Consider three mutually exclusive and exhaustive events and where:
. . .
What condition on must hold?
You are correct.
"Mutually exclusive" and "mutually exhaustive" means the sets have
. . no overlap, and together they "take up" the entire sample space.
The Venn diagram looks like this:
Code:* - - - - - - - * | | * A0 * | * * | | * * | | * * | | A1 * A2 | | | | * - - - * - - - *
Let represent the areas of their respective regions in the unit square.
. . . . .