Question

The probability that a patient visiting a dentist 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 ?

Answer 1

$p\left(E_1\right)=0.06,p\left(E_2\right)=0.2andP(E_1\cup E_2)=0.23$

$p(E_1\cap E_2)=p\left(E_1\right)+p\left(E_2\right)-p(E_1\cup E_2)=0.03$