Problem 42BB

Extending the Addition Rule Extend the formal addition rule to develop an expression for P(A or B or C ). (Hint: Draw a Venn diagram.)

Solution 42BB

P (A or B or C)

=P(A or B) or C)

=P(A or B) + P (C) - P (A or B) and C) (from additional rule)

=P (A) + P (B) - P (A and B) + P ( C) - {P((A and C) or (B and C))}

=P(A) + P (B) + P (C ) - P (A and B) - { P(A and C) + P (B and C)- P (A and B and C)

=P(A) + P (B) + P (C ) - P (A and B) - P (A and C) - P (B and C) + P (A and B and C)