Finding Probabilities Use the probability distribution you made in Exercise 19 to find the probability of randomly selecting a household that has (a) one or two HD televisions

Verified step by step guidance

1. Step 1: Recall the probability distribution created in Exercise 19. A probability distribution lists all possible outcomes (e.g., the number of HD televisions in a household) and their corresponding probabilities. Ensure that the probabilities sum to 1.
2. Step 2: Identify the outcomes of interest. In this case, we are looking for households with either one or two HD televisions. These correspond to the outcomes '1' and '2' in the probability distribution.
3. Step 3: Locate the probabilities associated with the outcomes '1' and '2' in the probability distribution. These probabilities are denoted as P(X=1) and P(X=2), where X represents the number of HD televisions.
4. Step 4: Add the probabilities of the outcomes '1' and '2' together to find the total probability. Use the formula: P(X=1 or X=2) = P(X=1) + P(X=2).
5. Step 5: Verify that the result is valid by ensuring it falls within the range of 0 to 1, as probabilities cannot exceed these bounds.

Key Concepts

Probability Distribution

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. It can be discrete, where outcomes are distinct and countable, or continuous, where outcomes can take any value within a range. Understanding how to construct and interpret a probability distribution is essential for calculating probabilities related to specific events.

Random Selection

Random selection refers to the process of choosing individuals or items from a population in such a way that each member has an equal chance of being selected. This concept is crucial in statistics as it helps ensure that the sample is representative of the population, allowing for valid inferences and conclusions. In the context of the question, it implies that each household has an equal opportunity to be chosen when assessing the number of HD televisions.

Event Probability

Event probability is the measure of the likelihood that a specific event will occur, expressed as a number between 0 and 1. In this case, it involves calculating the probability of selecting a household with one or two HD televisions based on the provided distribution. Understanding how to compute event probabilities is fundamental for making predictions and informed decisions based on statistical data.