According to United Airlines, its flight from Miami to San Fra n cisco is on tim

Question

According to United Airlines, its flight from Miami to San Fra n cisco is on time 90% of the time. Flight records are randomly selected over the year and examined to see if the flight landed on time to assess United Airlines. a. Find the probability that the frst fighton time s the fith fight selected. b. Find the probability that it takes at least 4 flights before selecting a flight that landed on time. c. Find the probability that the ninth flight on time is the tenth flight selected. d. On average, how many flights must be selected to find 10 on time flights.

Explanation / Answer

a) P(First flight on time is the fifth flight) = 0.1*0.1*0.1*0.1*0.9 = 0.00009

b) This is a geometric distribution,

P(Takes atleast 4 flights before selecting a flight that landed) = P(X >= 4) = 1- [1 - (1-p)k]= (1-0.9)3 = 0.001

c) P(9th flight on time is the 10th flight) = [9c8 * 0.98 * 0.1] * 0.9 = 0.3487

d) X*0.9 = 10
X = 11.11 flights

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