Answer :

Let A denote the event that a patient visiting a denist will have a tooth extracted and B denote the event that a patient will have a cavity filled


Given : P(A) = 0.06 , P(B) = 0.2 , P(A or B) = 0.23


To find: Probability that he will have a tooth extracted and a cavity filled= P(A and B)


Formula used : P(A or B) = P(A) + P(B) - P(A and B)


Probability that he will have a tooth extracted or a cavity filled = 0.23


0.23 = 0.06 + 0.2 P(A and B)


0.23 = 0.26 P(A and B)


P(A and B) = 0.26 – 0.23 = 0.03


P(A and B) = 0.03


Probability that he will have a tooth extracted and a cavity filled=P(A and B) = 0.03


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