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Intersection of Three events (probability)

  • Thread starter jchiz24
  • Start date
  • #1
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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
 

Answers and Replies

  • #2
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What you need is inclusion-exclusion principle. It's as true for probability as for cardinality.
 
  • #3
Dick
Science Advisor
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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?
 

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