Intersection of Three events (probability)

[jchiz24]

Homework Statement

Show that for 3 events A, B, C, the probability P of the intersection of A, B, and C is greater than or equal to P(A) + P(B) + P(C) - 2.

aka: P(A intersection B intersection C) > or = P(A) + P(B) + P(C) - 2

Homework Equations

N/R

The Attempt at a Solution

Use venn diagram, look at areas of venn diagram in terms of complement

 

[losiu99]

What you need is inclusion-exclusion principle. It's as true for probability as for cardinality.

 

[Dick]

In terms of your Venn diagram, label each area by how many times it is counted in P(A)+P(B)+P(C). The '-2' then subtracts each area twice. What do you conclude?