The following table contains data from a study of two airlines which fly to Smal

Question

The following table contains data from a study of two airlines which fly to Small Town, USA. If one of the 87 flights is randomly selected, find the probability that: a) The flight selected is an Upstate Airlines flight which was on time. b) The flight selected is a Podunk Airlines flight which was late c) The flight selected is an Upstate Airlines flight d) The flight selected was on time e) The flight selected is a Podunk Airlines flight given it arrived on time f) The flight selected is an Upstate Airlines flight or it arrived late

Explanation / Answer

                        on time            late       total

Podunk               33                    6        39

Upstate             43                     5         48

Total                  76                    11        86

(a) P(Upstae &on time) = 43/86 = 0.5

(b) P(Podunk & late) = 6/86 = 0.0698

(c) P(Upstate) = 48/86 = 0.5581

(d) P(on time) = 76/86 = 0.8837

(e) P(Podunk/ontime):

By multiplication theorem:

P(Podunk/ontime) P(ontime) = P(Podunk & ontime)

So,

P(Podunk/ontime) = P(Podunk & ontime)/P(ontime)

Now:
P(Podunk & ontime) = 33/86 = 0.3837

P(ontime) = 76/86 = 0.8837

Substituting, we get:
P(Podunk/ontime) = 0.3837/0.8837 = 0.4342

(f) P(Upstate OR late ) = P(Upstate) + P(late) - P(Upstate & late)

Now:
P(Upstate) = 48/86 = 0.5581

P(late) = 11/86 = 0.1279

P(Upstate & late) = 5/86 = 0.0581

Substituting, we get:
P(Upstate &or late) = 0.5581 + 0.1279 - 0.0581= 0.6279

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