Question

If a person visits his dentist, suppose the probability that he will have his teeth cleaned is 0.48, the probability that the will have cavity filled is 0.25, probability that he will have a tooth extracted is 0.20, the probability that he will have teeth cleaned and cavity filled is 0.09, the probability that he will have his teeth cleaned and a tooth extracted is 0.12, the probability that he will have as cavity filled and tooth extracted is 0.07, and the probability that he will have his teeth cleaned, cavity filled , and tooth extracted s 0.03. What is the probability that a person visiting his dentist will have at least one of these things done ot him? Select the correct answer from above options

Answer 1

A: teeth cleaned B:cavity filled C:tooth extracted P ( A ) = 0.48 , P ( B ) = 0.25 , P ( C ) + 0.2 P P ( A ∩ B ) = 0.09 , P ( B ∩ C ) = 0.07 , P ( A ∩ C ) = 0.12 P P ( A ∩ B ∩ C ) = 0.03 P P ( A ∪ B ∪ C ) = P ( A ) + P ( B ) + P ( C ) − P ( A ∩ B ) − P ( B ∩ C ) − P ( C ∩ A ) + P ( A ∩ B ∩ C ) P = 0.48 + 0.25 + 0.2 − 0.07 − 0.09 − 0.12 + 0.03 = = 0.68 = .