Earn More Than Your Parents?
In 1970, 92% of American 30-year-olds earned more than their parents did at age 30 (adjusted for inflation). In 2014, only 51% of American 30-year-olds earned more than their parents did at age 30. Source: Wall Street Journal, December 8, 2016.
b. What is the probability that two randomly selected 30-year-olds in 1970 earned more than their parents at age 30?

Verified step by step guidance

1. Identify the probability that a single 30-year-old in 1970 earned more than their parents at age 30. According to the problem, this probability is 0.92 (or 92%).
2. Since the problem asks for the probability that two randomly selected 30-year-olds both earned more than their parents, recognize that these are independent events assuming one person's earnings do not affect the other's.
3. Use the multiplication rule for independent events, which states that the probability of both events occurring is the product of their individual probabilities.
4. Set up the equation for the combined probability: \(P(\text{both earn more}) = P(\text{first earns more}) \times P(\text{second earns more})\).
5. Substitute the known probability values into the equation: \(P(\text{both earn more}) = 0.92 \times 0.92\).

Key Concepts

Probability of Independent Events

When two events are independent, the probability that both occur is the product of their individual probabilities. In this question, assuming each 30-year-old's earning status relative to their parents is independent, the combined probability is found by multiplying the probabilities for each individual.

Interpreting Percentage as Probability

Percentages can be converted into probabilities by dividing by 100. Here, 92% means a probability of 0.92 that a randomly selected 30-year-old in 1970 earned more than their parents, which is essential for calculating combined probabilities.

Contextual Understanding of Data

Understanding the context—such as the year, age group, and inflation adjustment—is crucial to correctly interpret the data and apply it to probability calculations. This ensures the probability reflects the specific scenario described in the question.