Answer to Question #152605 in Statistics and Probability for Arvin

Question

4. An insurance company classifies the airplane it insures into class L (low risk)
and class H (high risk), and estimates the corresponding proportions of
the airplane as 70% and 30% respectively. The company has also found that 99%
of class L and 88% of class H airplane have no accident within a year. If an
airplane insured by the company has no accident within a year, what is the
probability that it belongs to
(a) class H?
(b) class L?

Answer 1

Let L denote class low risk, H denote high risk and N denote no accident.

P(L) =0.7

P(H)=0.3

P(N|L)=0.99

P(N|H)= 0.88

a) P(H|N) =$\frac{P(H) P(N|H)} {P(H) P(N|H) +P(L) P(N|L) }$

=$\frac {0.3*0.88}{(0.3*0.88)+(0.7*0.99)}$

=0.2759

b) P(L|N) =$\frac{P(L) P(N|L)} {P(H) P(N|H) +P(L) P(N|L) }$

=$\frac {0.7*0.99}{(0.3*0.88)+(0.7*0.99)}$

=0.7241