ChatGPT Use According to Pew Research, 26% of U.S. teens ages 13 to 17 using ChatGPT for their schoolwork.


a. What is the probability that four randomly selected 13- to 17-year-olds all use ChatGPT for their schoolwork?

Verified step by step guidance

1. Identify the probability that a single randomly selected teen uses ChatGPT for their schoolwork. According to the problem, this probability is 26%, which can be written as \(p = 0.26\).
2. Since the problem asks for the probability that all four randomly selected teens use ChatGPT, recognize that these are independent events (assuming each teen's usage is independent of the others).
3. Use the multiplication rule for independent events, which states that the probability of all events occurring is the product of their individual probabilities.
4. Set up the expression for the probability that all four teens use ChatGPT as \(P = p \times p \times p \times p = p^4\).
5. Substitute the value of \(p\) into the expression to get \(P = (0.26)^4\). This expression represents the probability that all four teens use ChatGPT for their schoolwork.

Key Concepts

Probability of Independent Events

This concept involves calculating the likelihood that multiple independent events all occur. When events are independent, the probability of all happening together is the product of their individual probabilities. For example, if each teen independently has a 26% chance of using ChatGPT, the combined probability for four teens is 0.26 multiplied by itself four times.

Binomial Probability

Binomial probability deals with the number of successes in a fixed number of independent trials, each with the same probability of success. Although this question focuses on all four teens using ChatGPT, understanding binomial distribution helps in broader contexts where you might want to find probabilities of different numbers of users among a group.

Random Sampling

Random sampling means each individual is selected in a way that every member of the population has an equal chance of being chosen. This ensures that the probability calculations are valid because the sample represents the population without bias, making the assumption of independence reasonable.