You can use twoway tables to find conditional probabilities. Recall that conditional probability is the probability that some event (B) occurs given that some other event (A) has already occurred. The probability of B given A is written this way:
P(B, given A) = P(B  A)
EXAMPLE
Suppose that 338 middle school students were asked which was their dominant hand. Here the results are shown in the twoway table:

Dominant Hand 



Right  Left  Ambidextrous 


Grade  6th  99  9  2  110 
7th  90  31  0  121  
8th  93  11  3  107  


282  51  5  338 
With contingency tables, you can just look at the corresponding cells and column or row totals. For the probability of lefthanded and sixth grade, the frequency was 9. For the probability of lefthanded, there were 51 of the lefties. So, the answer is 9 out of 51.
Questions  Written as Conditional Probability  Conditional Probability Formula 

What is the probability that a seventhgrade student is ambidextrous?  What is the probability that a student is ambidextrous, given they are a seventh grader?  
What is the probability that a student who is righthanded is in eighth grade?  What is the probability that a student is in eight grade, given that he or she is righthanded? 
You can use a twoway table that actually has probabilities in it or relative frequencies.
EXAMPLE
A class of 10th graders was asked if they prefer cheese, pepperoni, or sausage pizza. The percentages are shown below: 41% of all of these kids are girls that enjoy cheese pizza, 12% of all of the kids are boys that enjoy pepperoni, etc.

Cheese  Pepperoni  Sausage 


Boy  0.05  0.12  0.19  0.36 
Girl  0.41  0.16  0.07  0.64 

0.46  0.28  0.26  1 
Source: Adapted from Sophia tutorial by Jonathan Osters.