Task
On April 15, 1912, the Titanic struck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Some believe that the rescue procedures favored the wealthier first class passengers. Data on survival of passengers are summarized in the table below. We will use this data to investigate the validity of such claims. (Data source: http://www.encyclopediatitanica.org/titanicstatistics.html)

Survived 
Did not survive 
Total 
First class passengers 
201 
123 
324 
Second class passengers 
118 
166 
284 
Third class passengers 
181 
528 
709 
Total passengers 
500 
817 
1317 

Are the events “passenger survived” and “passenger was in first class” independent events?
Support your answer using appropriate probability calculations.

Are the events “passenger survived” and“passenger was in third class” independent events? Support your answer using appropriate probability calculations.

Did all passengers aboard the Titanic have the same probability of surviving? Support your answer using appropriate probability calculations.
IM Commentary
This is the second task in the series of three, which ask related questions, but use different levels of scaffolding. Also, the third task uses a more detailed version of the data table. This task lets students explore the concepts of probability as a fraction of outcomes, and using twoway tables of data. The special emphasis is on developing their understanding of conditional probability and independence. Students should be able to use conditional probability to decide if two events $A$ and $B$ are independent; that is they should check if $P(A  B)=P(A)$, or if $P(B  A)=P(B)$.
In the last part of the task students have to decide which probabilities would be useful to answer the given question, and calculate them.
This task could be used as a group activity where students cooperate to formulate a plan of how to answer each question and calculate the appropriate probabilities. The task could lead to extended class discussions about the different ways of using probability to justify general claims (i.e. Can we really say that first class passengers had a greater chance of being rescued? Why or why not?)
The other tasks in this series are SCP.1,4,6 The Titanic 1 and SCP.4,5,6 The Titanic 3.