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# Tying ideas together

## • Interpret two-way frequency tables of data when two categories are associated with each object being classified, using the tables as a sample space in determining conditional probabilities and independence. • Construct two-way frequency tables, use them to determine probabilities, and interpret these probabilities in the context of the data.

Students apply their knowledge of conditional probability and independence in tasks which are less structured than earlier tasks in the unit.

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## Tasks

1 The Titanic 3

WHAT: This is the last task in the series of three about the Titanic, this one using a more detailed version of the data table. This is a very open ended task that notes, “Some believe that the rescue procedures favored the wealthier first class passengers. Others believe that the survival rates can be explained by the ‘women and children first’ policy,” and asks students to investigate what might or might not be concluded from the table. The special emphasis in this task again is on understanding of conditional probability and independence. This task could be used as a group activity where students cooperate to formulate a plan of how to answer the question and calculate the appropriate probabilities and could lead to extended class discussions about the different ways of using probability to justify general claims.

WHY: Students will need to synthesize their knowledge of conditional events and independence and the openness of this task will allow them to do this in a way that makes most sense to them. Because they will have to pose their own questions and then use the table correctly to reach a conclusion, their linking of conditional probability and independence could take many different forms. This task would most likely be used in lieu of "The Titanic 2" though a teacher may find a usefulness to implementing both successively in their classroom (MP.3).