Answer to Question #346092 in Statistics and Probability for ankit yadav

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 own time rate are 80% , 65% and 40% respectively.

·        Draw the probability tree diagram

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

Answer 1

Event A represents that scheduled flights for Airline Amira.

Event B represents that scheduled flights for Airline Biyas.

The event C represents that scheduled flights for Airline Chinar.

The event E represents that flight left in on time.

The prior probabilities are:

P(A)=0.50

P(B)=0.30

P(C)=0.20

The posterior probabilities are:

P(E|A)=0.80

P(E|B)=0.65

P(E|C)=0.40

So, the probability diagram:

We have to find the probability that it was airline A if the plane has just left on time.

That is, we have to find P(A|E)

Substituting the prior and likelihood (posterior) probabilities into the Bayes’s Law formula, then it yields

$P(A|E) = \frac{P(E|A) \times P(A)}{P(E|A) \times P(A) + P(E|B) \times P(B) + P(E|C) \times P(C)} \\ = \frac{0.80 \times 0.50}{0.80 \times 0.50 + 0.65 \times 0.30 + 0.40 \times 0.20} \\ = \frac{0.4}{0.675} \\ = 0.59259$

Therefore, the probability that it was airline A if the plane has just left on time is 0.593.