The probability that a patient visiting a denist will have a tooth extracted is 0.06, the probability that he will have a cavity filled is 0.2, and the probability that he will have a tooth extracted or a cavity filled is 0.23.What is the probability that he will have a tooth extracted as well as a cavity filled?

Question

Philoid · Accepted 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