Question

Three airlines serve a Srinagar. Airline 'Amira' has 50% of all the scheduled flights, airline 'Biyas' has30% and airline 'chinar' has the remaining 20%. Their on-time rates are 80%, 65%, and 40%, respectively.

Part 2) A plane has just left on time. What is the probability that it was airline 'Amira'.

Answer 1

$H_1-Amira,H_2-Biyas,H_3-Chinar\\A-on\,\,time\\P\left( H_1 \right) =0.5,P\left( H_2 \right) =0.3,P\left( H_3 \right) =0.2\\P\left( A|H_1 \right) =0.8,P\left( A|H_2 \right) =0.65,P\left( A|H_3 \right) =0.4\\P\left( H_1|A \right) =\frac{P\left( A|H_1 \right) P\left( H_1 \right)}{P\left( A|H_1 \right) P\left( H_1 \right) +P\left( A|H_2 \right) P\left( H_2 \right) +P\left( A|H_3 \right) P\left( H_3 \right)}=\\=\frac{0.8\cdot 0.5}{0.8\cdot 0.5+0.65\cdot 0.3+0.4\cdot 0.2}=0.592593$