Step 1 :Given that the number of passengers who survived is 232 and the total number of passengers is 1865.
Step 2 :To find the probability that a passenger survived, we need to divide the number of passengers who survived by the total number of passengers.
Step 3 :Using the formula for probability, \(P(A) = \frac{n(A)}{n(S)}\), where \(n(A)\) is the number of successful outcomes and \(n(S)\) is the total number of outcomes.
Step 4 :Substituting the given values into the formula, we get \(P(A) = \frac{232}{1865}\).
Step 5 :Calculating the above expression, we get \(P(A) = 0.12439678284182305\).
Step 6 :Rounding to three decimal places as needed, we get \(P(A) = 0.124\).
Step 7 :Final Answer: The probability that a passenger survived is approximately \(\boxed{0.124}\).