The following represent the results of a survey in which individuals were asked to disclose what they perceive to be the ideal number of children.
b. What is the probability an individual is female and believes the ideal number of children is 2?

Verified step by step guidance

1. Step 1: Identify the total number of individuals surveyed. This is given in the bottom right corner of the table, which is 297.
2. Step 2: Identify the number of individuals who are female and believe the ideal number of children is 2. From the table, this value is 87.
3. Step 3: Understand that the probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Here, the event is 'individual is female and believes the ideal number of children is 2'.
4. Step 4: Write the probability formula for this event as: \(P(\text{Female and ideal number of children is 2}) = \frac{\text{Number of females who prefer 2 children}}{\text{Total number of individuals}}\).
5. Step 5: Substitute the values from the table into the formula: \(P = \frac{87}{297}\). This fraction represents the probability asked for in the problem.

Key Concepts

Joint Probability

Joint probability refers to the likelihood of two events occurring simultaneously. In this context, it is the probability that an individual is both female and prefers a specific number of children. It is calculated by dividing the count of individuals meeting both criteria by the total number of individuals surveyed.

Contingency Table Interpretation

A contingency table displays the frequency distribution of variables and their combinations. Understanding how to read the rows and columns allows one to identify counts for specific groups, such as females who prefer 2 children, which is essential for calculating probabilities.

Probability Calculation from Frequency Data

Calculating probability from frequency data involves dividing the number of favorable outcomes by the total number of outcomes. Here, the probability that an individual is female and prefers 2 children is the frequency of females preferring 2 children divided by the total survey population.