1.

If a person visits his dentist, suppose the probability that he will have his teeth cleaned is 0.48, the probability that he will have a cavity filled is 0.25, the probability that he will have a tooth extracted is 0.20, the probability that he will have a teeth cleaned and a 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 a cavity filled and a tooth extracted is 0.07, and the probability that he will have his teeth cleaned, a cavity filled, and a tooth extracted is 0.03. What is the probability that a person visiting his dentist will have at least one of these things done to him?

Answer»

Let C be the event that the person will have his teeth cleaned and F and E be the event of getting cavity filled or tooth extracted, respectively. We are given

P(C) = 0.48, P (F) = 0.25, P (E) = .20, P (C ∩ F) = .09,

P (C ∩ E) = 0.12, P (E ∩ F) = 0.07 and P (C ∩ F ∩ Ε) = 0.03

Now, P ( C ∪ F ∪ E) = P (C) + P (F) + P (E) – P (C ∩ F) – P (C ∩ E) – P (F ∩ E) + P (C ∩ F ∩ E)

= 0.48 + 0.25 + 0.20 – 0.09 – 0.12 – 0.07 + 0.03 = 0.68


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