Answer to Question #327184 in Statistics and Probability for Sneha

Question

Three airlines serve a Srinagar. Airline ‘Amira’ has 50% of all the scheduled flights, airline ‘Biyas’ has 30%, and airline ‘chinar’ has the remaining 20%. Their on-time rates are 80%, 65%, and 40%, respectively. 

A plane has just left on time. What is the probability that it was airline ‘Amira’? 

Answer 1

Let A₁, A₂, and A₃ represent the events of the flight was of Amira, Biyas and Chinar respectively, and let B be the event 'The flight left on time'.

Then we are to find the value of P(A₁|B).

Using Bayes’ theorem formula we get:

$P(A_1|B)=\\ =\cfrac{P(B|A_1)P(A_1)}{P(B|A_1)P(A_1)+P(B|A_2)P(A_2)+P(B|A_3)P(A_3)}=\\ =\cfrac{0.80\cdot0.50}{0.80\cdot0.50+0.65\cdot0.30+0.40\cdot0.20}=\\ =0.5926.$