Two way tables are used to display information. They can be used to find probabilities too. The two way table below shows information about the methods people go to school.
Walk 
Bus 
Train 
Car 
Total 

Boy 
290 
131 
52 
101 
574 
Girl 
408 
49 
13 
144 
614 
Teacher 
2 
1 
5 
32 
40 
Total 
700 
181 
70 
277 
1228 
Notice that the entries in each row add up to the total in the rightmost column, so that in the row labelled 'Boy', 290+131+52+101=584 and the entries in each column add up to the total given in the bottom row, so that fro the column labelled 'Walk', 290+408+2=700.
If we wanted to find the probability that a person picked at random was a boy who walked to school, we would divide the number of boys who walk to schools by the total number of people, obtaining
If we wanted to find the probability that a person picked at random travelled by car to school, we would divide the number of people who travelled by car by the total number of people, obtaining
If we had a partially completed table, we can often complete it using the fact that the rows add to give the rightmost entry and the columns add to give the entries in the bottom row. Suppose we have the partially completed table below.
Walk 
Bus 
Train 
Car 
Total 

Boy 
290 
131 
574 

Girl 
49 
13 
144 

Teacher 
2 
32 
40 

Total 
181 
70 
277 
We complete the table by looking for rows or columns with single missing entries, one at a time, indicated in green.
Walk 
Bus 
Train 
Car 
Total 

Boy 
284 
136 
592 

Girl 
48 
12 
149 
654 

Teacher 
2 
6 
32 
46 

Total 
190 
87 
284 
Walk 
Bus 
Train 
Car 
Total 

Boy 
284 
136 
592 

Girl 
48 
12 
149 
654 

Teacher 
2 
6 
6 
32 
46 
Total 
190 
87 
284 
Walk 
Bus 
Train 
Car 
Total 

Boy 
284 
136 
69 
592 

Girl 
48 
12 
149 
654 

Teacher 
2 
6 
6 
32 
46 
Total 
190 
87 
284 
Walk 
Bus 
Train 
Car 
Total 

Boy 
284 
136 
69 
103 
592 
Girl 
48 
12 
149 
654 

Teacher 
2 
6 
6 
32 
46 
Total 
190 
87 
284 
Walk 
Bus 
Train 
Car 
Total 

Boy 
284 
136 
69 
103 
592 
Girl 
445 
48 
12 
149 
654 
Teacher 
2 
6 
6 
32 
46 
Total 
190 
87 
284 
Walk 
Bus 
Train 
Car 
Total 

Boy 
284 
136 
69 
103 
592 
Girl 
445 
48 
12 
149 
654 
Teacher 
2 
6 
6 
32 
46 
Total 
731 
190 
87 
284 
Walk 
Bus 
Train 
Car 
Total 

Boy 
284 
136 
69 
103 
592 
Girl 
445 
48 
12 
149 
654 
Teacher 
2 
6 
6 
32 
46 
Total 
731 
190 
87 
284 
1292 