# Constructing joint frequency tables for North-South Railways

The new GM of North-South Railways initiated a drive to make sure that trains do run on time. He had collected data on 200 instances where the trains arrived late at the destination. Of these, 160 started late (SL) at the origin itself, where as the remaining 40 did start on time (SO), but reached the destination late. He had grouped various reasons causing the delay into 3 categories namely Infrastructure (I), Train Crew (C) and Rolling stock (R). He found that half of the 200 instances can be attributed to Infrastructure where as only 40 could be attributed to Rolling stock. 25 percent of the trains that started late (SL) at the origin itself were attributed to Crew. Same percentage of the 40 trains that started on time (SO) were attributed to rolling stock.

Construct the joint frequency table and answer following questions:

1. What is the probability that the delay is because of the Crew?

2.What is the probability that the train started on time but reached the destination late, given that the reason for the delay is because of the infrastructure?

3. Are the two events "Starting on time" and "Infrastructure" independent of each other? Explain.