# The probability that a patient visiting a denist will have a tooth extracted is 0.06, the probability

Question:

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?

Solution:

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 $B)=0.03$