probability question

Question

Adarsh Sharma, supervisor of customer relations for Fly High airlines at Delhi Airport, is studying the problem of customer inconvenience due to flight delays. He is concentrating on three late-night flights out of Indira Gandhi International (IGI) Airport in New Delhi, In the last year, 7, 8, and 5 percent of the London, New York, and Singapore flights, respectively have been delayed. Further, 55, 20, and 25 percent of the late-night Fly High at IGI are for London, New York, and destinations, respectively. What is the probability that a delayed flight was scheduled for (a) London, (b) New York, and (c) Singapore?

Answer 1

Let's suppose that 10000 late-night flights from IGI airport were investigated. So there were 5500 London, 2000 New York and 2500 Singapore flights, 

Of the 5500 to London, 7% are delayed=385 flights.

Of the 2000 to New York, 8% are delayed=160 flights.

Of the 2500 to Singapore, 5% are delayed=125 flights.

In all, 670 flights were delayed (out of 10000 flights---6.7%). So, given that a flight was delayed, the following probabilities can be calculated (approximate percentages):

(a) 385/670=57.46% (London)

(b) 160/670=23.88% (New York)

(c) 125/670=18.66% (Singapore)