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Question
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 atleast one of these things done to him?
Solution
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) = 0.20
P(C ∩ F) = 0.09
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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