An airline pricing analyst has been asked to review a struggling airline’s fligh

Question

An airline pricing analyst has been asked to review a struggling airline’s flights. She has determined that 60% of all flights are profitable to the company after paying pilot, flight attendants, food, fuel, operations costs, etc. When seat utilization of a flight meets the industry average, the flight is profitable 80% of the time. The probability of a flight being profitable and not meeting the seat utilization industry average is 20%.

If the flight is not profitable, what is the probability it did not meet the industry average for seat utilization?

Explanation / Answer

let probability of being profitable =P(A) and that of meeting the seat utilization industry average =P(B)

here P(A) =0.60

and P(A|B) =0.8

probability of a flight being profitable and not meeting the seat utilization industry average is =P(AnBc)=0.20

here P(AnB) =P(A)-P(AnBc) =0.6-0.20=0.40

from above P(B) =P(AnB)/P(A|B) =0.4/0.8 =0.5

hence P(AcnBc) = 1-P(AUB) =1-(P(A)+P(B)-P(AnB) =1-(0.6+0.5-0.40)=0.3

therefore  probability it did not meet the industry average for seat utilization=P(Bc|Ac) =P(AcnBc) /P(Ac)

=0.3/(1-0.6)=3/4=0.75

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