Airlines Probability Calculation

What is the probability that your friend was flying on airline B?

Your friend's flight just left the airport late. Calculate the probability that your friend was flying on airline B.

Final answer:

The probability that your friend was flying on airline B given that their flight left the airport late is approximately 0.282.

To find the probability that your friend was flying on airline B given that their flight left the airport late, we can use conditional probability. Let's denote the events as follows:

  • A: Flying on airline A
  • B: Flying on airline B
  • C: Flying on airline C
  • L: Flight left the airport late

We are given the following probabilities:

  • P(A) = 0.47
  • P(B) = 0.30
  • P(C) = 0.23
  • P(L|A) = 0.16
  • P(L|B) = 0.35
  • P(L|C) = 0.56

Using Bayes' theorem, we can calculate the probability of flying on airline B given that the flight left the airport late:

P(B|L) = (P(L|B) * P(B)) / (P(L|A) * P(A) + P(L|B) * P(B) + P(L|C) * P(C))

Substitute the given values into the equation to find:

P(B|L) ≈ 0.282

Therefore, the probability that your friend was flying on airline B is approximately 0.282.

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