Flights arriving to DTW might be national or international. Assume that one out of every five national flights is followed by an international flight. If in the long run 25 percent of the flights are national, what fraction of international flights are directly followed by a national flight

1/15

Step-by-step explanation:

Given

1 out of every 5 national flight is followed by an international flight.

p = 1/5

q = 1 - p

q = 1 - 1/5

q = 4/5

π0 = 0.25

We want to determine

p:the fraction of international flights that are followed by a national flight.

Let X = 0

If the nth flight is national

Let X = 1

if the flight is international

This gives rise to a two state Markov chain with transition probability as follows

P = (4/5. 1/5. p. 1-p)

The long run proportion are the below solution gotten from the Markov chain above

π0 = 4/5π0 + pπ1 1

π1 = 1/5π0 + (1 - p)π1 2

π0 + π1 = 1 . 3

Solving the above equations,

We have

Substitute 0.25 for π0 in (3)

0.25 + π1 = 1

π1 = 1 - 0.25

π1 = 0.75

Solving 1 and 3

Substitute 0.75 for π1 and 0.25 for π0 in (1)

0.25 = 4/5 * 0.25 + 0.75p

0.25 = 0.2 + 0.75p

0.75p = 0.25 - 0.2

0.75p = 0.05

p = 0.05/0.75

P = 1/15 or 0.0667(6.67%)

So, one out of every 15 international flights is followed by a national flight (or 6.66 percent)

where is the figure

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,