Step 1 :Given the data, we are asked to find the probability of survival for a female passenger and a child passenger.
Step 2 :First, let's calculate the probability for a female passenger. The total number of passengers is 1942, and the total number of females is 468. Out of these, 396 females survived.
Step 3 :The probability of an event A given that another event B has occurred is given by P(A|B) = P(A ∩ B) / P(B). In this case, event A is survival and event B is being a female.
Step 4 :We calculate P(A ∩ B) by dividing the number of surviving females by the total number of passengers, which gives us \(\frac{396}{1942} = 0.203913491246138\).
Step 5 :P(B) is the total number of females divided by the total number of passengers, which gives us \(\frac{468}{1942} = 0.24098867147270855\).
Step 6 :Using these values, we find that P(A|B) for a female passenger is \(\frac{0.203913491246138}{0.24098867147270855} = 0.846\).
Step 7 :So, the probability that a female passenger survived is \(\boxed{0.846}\).
Step 8 :Next, let's calculate the probability for a child passenger. The total number of children is 132, and out of these, 79 children survived.
Step 9 :We calculate P(A ∩ B) by dividing the number of surviving children by the total number of passengers, which gives us \(\frac{79}{1942} = 0.040679711637487126\).
Step 10 :P(B) is the total number of children divided by the total number of passengers, which gives us \(\frac{132}{1942} = 0.06797116374871266\).
Step 11 :Using these values, we find that P(A|B) for a child passenger is \(\frac{0.040679711637487126}{0.06797116374871266} = 0.598\).
Step 12 :So, the probability that a child passenger survived is \(\boxed{0.598}\).