On April 15, 1912, the Titanic struck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Data on survival of passengers are summarized in the table below. (Data source: http://www.encyclopedia-titanica.org/titanic-statistics.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 |
Calculate the following probabilities. Round your answers to three decimal places.
There are many questions that can be answered using the given table. Possible answers may include, but are not limited, to the following:
If one of the passengers is randomly selected, what is the probability that this passenger was in second class?
Answer: \(P(\text{passenger was in second class})= \frac{284}{1317} \approx 0.216\).
If one of the passengers is randomly selected, what is the probability that this passenger was in second class and survived?
Answer: \(P[\text{(passenger was in second class) and (passenger survived)}]= \frac{118}{1317} \approx 0.090.\).
If one of the passengers is randomly selected from among the second class passengers, what is the probability that this passenger survived?
Answer: \(P(\text{passenger survived | passenger was in second class}) = \frac{118}{284} \approx 0.415\).
If one of the passengers who survived is randomly selected, what is the probability that this passenger was in second class?
Answer: \(P(\text{passenger was in second class | passenger survived}) = \frac{118}{500} \approx 0.236\).
Commentary
This is the first 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 guides students by asking the series of specific questions and lets them explore the concepts of probability as a fraction of outcomes, and using two-way tables of data. The emphasis is on developing their understanding of conditional probability. Students should understand the difference between \(P(A \text{ and } B)\) and \(P(A | B)\), and notice that \(P(A | B)\) is not the same as \(P(B | A)\). Parts b and c require students to verbalize their understanding of probability. The last part of the task is open ended, and there are many possible questions we could ask, and answer, using the given table. For example, questions could be posed about second class passengers.
The task could lead to extended class discussions about the chances of events happening, and differences between unconditional and conditional probabilities. Special emphasis should be put on understanding what the sample space is for each question.
The other tasks in this series are S-CP.3,4,5,6 The Titanic 2 and S-CP.4,5,6 The Titanic 3.