What are two-way tables?

• While?Venn?diagrams?are great at showing?overlap?they can only show one feature (characteristic) of a situation at one time
• In the notes on Venn diagrams we had an example talking about students studying either Spanish or German, or bothHowever we may?also?be interested in how many?boys?and?girls?were studying Spanish and/or German as well
• This is where we need a two-way table – one of the?characteristics?will be the columns and the other will be presented in rows
• Once we have our table we can use the numbers within to determine probabilities

What do I need to know?

• You’ll need to be able to construct a two-way table from information given in words and then use a table to calculate probabilities
• So you’ll need to be familiar with the basics and notation around probability

1. Total row/column

• It may not be obvious from the wording but a total row and column can be really helpful in two-way table questions
• If they’re not mentioned, or included when given a table, add them in

2. Completing a?table

• It may not be possible to add numbers to the table from every sentence, one at a time
• You will usually have to combine one piece of information with another in order to fully complete a table

3. Conditional probability

• Two-way tables in particular give rise to using?conditional?probability
• This can get complicated but with two-way tables, it is usually straightforward to see which parts of the table the question is referring to