Titanic Survivors The following data represent the survival data for the ill-fated Titanic voyage by gender. The males are adult males and the females are adult females.
a. What is the probability that the passenger survived?

Verified step by step guidance

1. Step 1: Identify the total number of passengers on the Titanic. This is given in the 'Total' row and 'Total' column of the table, which sums all passengers regardless of survival status.
2. Step 2: Identify the total number of passengers who survived. This is given in the 'Survived' row and 'Total' column of the table, which sums all survivors across all categories.
3. Step 3: Recall the formula for probability of an event, which is the number of favorable outcomes divided by the total number of possible outcomes. In this case, the event is 'survived'. The formula is: \(\\text{P(survived)} = \frac{\\text{Number of survivors}}{\\text{Total number of passengers}}\)
4. Step 4: Substitute the values from the table into the formula. Use the total survivors from Step 2 as the numerator and the total passengers from Step 1 as the denominator.
5. Step 5: Simplify the fraction to express the probability. This will give the probability that a randomly selected passenger survived the Titanic disaster.

Key Concepts

Probability

Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this question, the probability of survival is found by dividing the total survivors by the total passengers.

Sample Space and Events

The sample space is the set of all possible outcomes, here the total number of passengers (2224). An event is a subset of the sample space, such as surviving the Titanic. Understanding these helps in correctly identifying the numerator and denominator when calculating probabilities.

Data Interpretation from Contingency Tables

Contingency tables organize data into categories, showing frequencies for combinations of variables. Interpreting such tables involves summing relevant counts to find totals for events, like total survivors or total passengers, which is essential for calculating probabilities accurately.