Titanic survival. Of the 2201 passengers on the RMS Titanic, only 711 survived. The practice of “women and children first” was first used to describe the chivalrous actions of the sailors during the sinking of the HMS Birkenhead in 1852, but became popular after the sinking of the Titanic, during which 53% of the children and 73% of the women survived, but only 21% of the men survived.

Part of the protocol stated that passengers enter lifeboats by ticket class as well. Here is a table showing survival by ticket class.

a) Find the conditional probability of survival for each type of ticket.

b) Draw a probability tree for this situation.

c) Given that a passenger survived, what is the probability they had a first-class ticket?

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Survival Class First Second Third Crew Total Alive 203 118 178 212 711 28.6% 16.6% 25.0% 29.8% 100% Dead 122 167 528 673 1490 8.2% 11.2% 35.4% 45.2% 100%