Answer:
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)
