COUNTRY ROADS OR NATIONAL HIGHWAY

You are travelling to the office daily by car. You can choose either village roads or national highway. Country roads do not have traffic, but it takes 60 minutes to reach office. Highway takes only 45 minutes. If there is a traffic jam, it takes as much as 90 minutes. which road will you choose?

Let us use a little math. Your experience suggests that there is a 1 in 5 chance that you will end up in a jam. That is, 20% or .20 chance to face a heavy traffic in the highway. That also implies that 80% of the time, there will only light traffic. If you travel daily for year on the highway, what is the average expected time of travel.

Expected time of travel
= (chance for light traffic*Normal time of travel) + (chance for heavy traffic *extended time)
=0.8*45+0.2*90
=54 minutes.

It is still 6 minutes less than the time taken by country roads (60mts). But there will be large saving of time in a year. Hence, it is advisable to take the national highway always.
Suppose there is 90% chance for light traffic, then,
=0.9*45+0.10*90
=40.4+9=49.4
Now it is 10 minutes less than the village roads.

This 'travelling ' can be simulated in a computer. That little 'program' is given here in plain English.

SUM = 0

Do 600 times the following- back and forth, for 1 year
    1. Generate a random number between 0 and 1.
    2. If the number is less than 0.8, SUM +SUM + 45 (light traffic) ELSE
   SUM = SUM +90 (heavy traffic)
END LOOP
Average time = SUM/600
Print average time.

The average time will be around 54 minutes. You can check it up, if you know little programming.
The computer simulation tells us that on the long run, we get theoretical results practically. You cannot expect time saving within a week of travel. That is the principle of probability and statistics.

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