Final answer:
A table represents a probability if all values are between 0 and 1, and the total sums up to 1. Probability contingency tables organize observed data into probabilities, facilitating the calculation of different types of probabilities. Completion of such a table involves transforming frequencies into probabilities that reflect the likelihood of various outcomes.
Step-by-step explanation:
To determine if a table represents a probability, we need to ensure that the numbers in the table satisfy two main conditions: the sum of all probabilities must equal 1, and no individual probability should be less than 0 or greater than 1. In a probability contingency table, the data is organized to present the probability of various outcomes relative to two variables that may affect each other. If the table includes observed frequencies, such as the number of televisions in households, we convert these frequencies to probabilities by dividing them by the total number of observations, and then we can check if these satisfy the conditions of probabilities. To complete a probability contingency table, one typically calculates probabilities for each category, makes sure the probabilities add up to 1, and answers questions related to marginal, joint, and conditional probabilities such as the likelihood of a randomly selected child having a specific hair color or texture.
For example, to find the probability of a child having wavy brown hair, we would identify the frequency of wavy brown hair in the table, divide by the total number of observations, and place this probability in the appropriate cell of the table. The practice of using such a table also covers the concepts of mutually exclusive events, such as choosing different doors in a game, where the probability of each must sum to 1. The principles of probability distributions dictate that the probabilities of all possible outcomes must sum to 1, which is often represented in summarized forms in probability distribution functions (PDFs).