A business man must travel to five different destinations ea

A business man must travel to five different destinations each year. He takes three flights to reach each of these destinations. Suppose that the first flight is on time 44% of the time, the second flight is on time 11.3% of the time and the third flight is on time 45% of the time. Also suppose the flight arrivals are independent.

(a) Let X be the number of times the first flight is on time for his five trips during the year. What are the mean and variance of X?

(b) What is the probability that the business man\'s second flight is on time for exactly three of his trips during the year?   

Solution

A business man must travel to five different destinations each year. He takes three flights to reach each of these destinations. Suppose that the first flight is on time 44% of the time, the second flight is on time 11.3% of the time and the third flight is on time 45% of the time. Also suppose the flight arrivals are independent.

(a) Let X be the number of times the first flight is on time for his five trips during the year. What are the mean and variance of X?

p=0.44

n=5

mean = Expectation = np = 2.2

Variance = np(1 - p) = 1.232

(b) What is the probability that the business man\'s second flight is on time for exactly three of his trips during the year?   

p=0.113

n=3

P(X=x) = (_nC_x) p^x (1-p)^n-x   

P(X=3) = (₃C₃) 0.113³ (1-0.113)^3-3   

= 0.0014