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.

What is the probability that the business man\'s third flight is on time for at least two of his trips during the year?

In two years, what is the probablity that the business man\'s first flight is on time exactly five times?

Solution

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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 48% of the time, the second flight is on time 10.6% of the time and the third flight is on time 41% of the time. Also suppose the flight arrivals are independent.

(a) What is the probability that the business man\'s third flight is on time for at least two of his trips during the year?

(b) In two years, what is the probablity that the business man\'s first flight is on time exactly five times?

ans

(a) What is the probability that the business man\'s third flight is on time for at least two of his trips during the year?
Let T be the event that the third trip is on time
P(x >=2) = 1-P(x<=1)
This can be approximated using the binomial distribution with
p = .41
n=5
x=1
1
0.31989833
0.68010167
(b) In two years, what is the probablity that the business man\'s first flight is on time exactly five times?
This can be approximated using the binomial distribution with
p = .48
n=10
x=5
0.671179546

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