There are four major air carriers with flights from Boston to L.A. 32% of all pa

Question

There are four major air carriers with flights from Boston to L.A. 32% of all passengers take American Airlines, 25% take Jet Blue, 17% take United, and 26% take Virgin America. Data from 2012 indicate that 20% of all American Airlines flights from Boston to L.A. are late, 23% of Jet Blue flights from Boston to L.A. are late, 19% of United flights from Boston to L.A. are late, and 11% of Virgin America flights from Boston to L.A. are late. Suppose a passenger taking a flight from Boston to L.A. is randomly selected.

a.) What is the probability that the passenger takes American Airlines and is late?

b.) What is the probability that the passenger is late? On time?

c.) Suppose the passenger arrives late. Which airline did the passenger most likely fly?

Explanation / Answer

a.) the probability that the passenger takes American Airlines and is late = P(that the passenger takes American Airlines)* P(American Airlines is late) = 0.32*0.20 = 0.064 = 6.4%

b.) the probability that the passenger is late = P(takes American Airlines)*P(American Airlines is late) + P(takes Jet Blue)*P(Jet Blue is late) +......

= 0.32*0.20 + 0.25*0.23 + 0.17*0.19 + 0.26*0.11 = 0.064 + 0.0575+ 0.0323 + 0.0286 = 0.1824 = 18.24%

P(On time) = 1 - P(Late) = 1-0.1824 = 0.8176 = 81.76%

c.) See the four terms in the previous part b.

The is maximum chance of being late is associated with American Airlines

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