Question

Three airlines serve a small town in Ohio. Airline A has 50% of all the scheduled flights, airline B has 30%, and airline C 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 A?

Answer 1

Answer:

0.5926

Step-by-step explanation:

given that three airlines serve a small town in Ohio. Airline A has 50% of all the scheduled flights, airline B has 30%, and airline C has the remaining 20%

i.e. A,B,C are mutually exclusive and exhaustive events as there is no other flight than these three.

Flight                  Prob         Time rates prob       Combined prob

A                          0.50                   0.80                     0.5*0.8 =0.40

B                           0.30                   0.65                     0.3*0.65 = 0.195

C                          0.20                    0.40                     0.2*0.4=0.08

Total                                                                           = 0.675

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

= P(A/time) = Pr of time and A/Prob of time

= $\frac{0.4}{0.675} \\=0.5926$

Answer is 0.5926