Airlines Probability Analysis

What is the probability that a plane leaving on time is from airline 'Amira'?

Given that airline 'Amira' has 50% of scheduled flights with an on-time rate of 80%.

What calculation can be made to determine the probability?

Probability Calculation:

Using Bayes' theorem, we can calculate the probability that a plane leaving on time is from airline 'Amira'.

In the given scenario, let A be the event that the plane is from airline 'Amira' with P(A) = 0.5, and let O be the event that the plane has left on time with P(O|A) = 0.8.

By applying Bayes' theorem, we can calculate the probability that the plane is from airline 'Amira' given that it has left on time:

P(A|O) = (P(O|A) × P(A)) / (P(O|A) × P(A) + P(O|B) × P(B) + P(O|C) × P(C))

Substitute the values into the formula:

P(A|O) = (0.8 × 0.5) / (0.8 × 0.5 + 0.65 × 0.3 + 0.4 × 0.2)

After calculation, the probability that a plane leaving on time is from airline 'Amira' is 0.541, or approximately 54.1%.