Question

question 1
the titanic struck an iceberg and sank on its first voyage across the atlantic in 1912. some passengers got off the ship in lifeboats, but many died. the two - way table gives information about adult passengers who survived and who died, by class of travel.

suppose we randomly select one of the adult passengers who rode on the titanic.

a) given that the person selected was in first class, whats the probability that he or she survived?
b) if the person selected survived, whats the probability that he or she was not a third - class passenger?

Explanation:

Step1: Calculate total first - class passengers

Total first - class passengers \(=197 + 122=319\)

Step2: Calculate probability for part (a)

Using the formula for conditional probability \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Here, \(A\) is'survived' and \(B\) is 'first - class'. So \(P(\text{survived}|\text{first - class})=\frac{197}{197 + 122}=\frac{197}{319}\approx0.617555\)

Step3: Calculate total survived passengers

Total survived passengers \(=197+94 + 151=442\)

Step4: Calculate non - third - class survived passengers

Non - third - class survived passengers \(=197+94 = 291\)

Step5: Calculate probability for part (b)

Using the formula for conditional probability \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Here, \(A\) is 'not third - class' and \(B\) is'survived'. So \(P(\text{not third - class}|\text{survived})=\frac{197 + 94}{197+94 + 151}=\frac{291}{442}\approx0.658371\)

Answer:

a) \(\frac{197}{319}\approx0.618\)
b) \(\frac{291}{442}\approx0.658\)