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

Guest Mar 10, 2022

#1**0 **

"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.

geno3141 Mar 10, 2022