Two parents plan to have three children. What is the probability that the children will be two girls and one boy?

Key Concepts

Probability Basics

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In genetics, it often involves calculating the chances of specific outcomes based on known ratios, such as the likelihood of having a boy or a girl. For two parents, the probability of having a boy or a girl is typically considered equal, at 0.5 for each.

Binomial Distribution

The binomial distribution is a statistical method used to model the number of successes in a fixed number of independent trials, each with the same probability of success. In this context, having a girl can be considered a 'success,' and the distribution helps calculate the probability of having a specific number of girls (successes) in a set number of children (trials).

Combinatorial Analysis

Combinatorial analysis involves counting the number of ways to arrange or select items from a set. In the context of the question, it helps determine the different arrangements of two girls and one boy among three children. The formula for combinations can be used to find how many unique ways these children can be arranged, which is essential for calculating the overall probability.