The probability that a flight, provided by airline company "Derry-air" operating on the route Homersville to Springfield, arrives late is p=0.22. If flights are independent, and a sample of 10 flights are taken what is the probability that at most one will arrive late

 Mar 10, 2022

"At most one will arrive late" means that either:

1)  all will arrive on time, or

2)  one will be late.


The probability that any one plane arrives on time is 1.00 - 0.22  =  0.78.

1)  all ten arriving on time  =  (0.78)10

2)  one will be late but nine arrive on time  =  10 x (0.22)1 x (0.78)9

          [the factor of 10 is used because the one that arrives late can be

           the first plane or the second plane or ... the tenth plane; ten ways]


To get the final answer, calculate the two individual probabilities and add them together.

 Mar 10, 2022

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