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In 1912, the RMS Titanic, a British passenger ship, sank in the North Atlantic Ocean after colliding with an iceberg. Historians do not know the exact passenger list, so the death toll is estimated. Here is data from the 2201 passengers on board, by cabin class. First Class Second Class Third Class Crew Row Totals Died 122 167 528 673 1490 Survived 203 118 178 212 711 Col Totals 325 285 706 885 2201 Source: Wikipedia, RMS Titanic (2015) If we randomly select a passenger who survived the Titanic, what is the probability that this passenger is in a second class cabin?

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aramisdegaula1977

Answer:

The probability that a surviving passenger belongs to second-class cabin passengers is [tex]\frac{118}{285} = 0.414[/tex]

Step-by-step explanation:

Let's define the events:

S: The passenger survived.

NS: The passenger did NOT survive.

C2: The passenger belonged to a second class cabin.

NC2: The passenger did not belong to a second class cabin.

With these events and the information provided the probability are:

[tex]P (S) = 711/2201[/tex]

[tex]P(NS) = 1490/2201[/tex]

[tex]P(C2) = 285/2201[/tex]

[tex]P (NC2) = 1495/2201[/tex]

The probability that a surviving passenger belongs to second-class cabin passengers is:

[tex]P (S | C2) = \frac{P(S\bigcapC2)}{P(C2)} = \frac{\frac{118}{2201}}{\frac{285}{2201}} = \frac{118}{285} = 0.414[/tex]

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