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A probability table is a simple yet powerful tool used to represent a probability distribution. In this case, the table lists the number of items a customer might select at a convenience store and their corresponding probabilities. Each row in the table represents a potential outcome (the number of items selected) and its likelihood.

Creating a probability table involves two key components:

• The first column lists each possible outcome, such as the number of items selected: 1, 2, 3, 4, and 5.
• The second column lists the probability of each outcome occurring, given here as 0.32, 0.12, 0.23, 0.18, and 0.15.

The probability table concisely shows the relationship between each event and its probability, making it easier to visualize and understand the data.

This structured approach ensures that students can easily follow and apply the information, laying the groundwork for deeper comprehension of probability concepts.

A bar graph is a visual representation of data that shows comparisons among different categories. Here, we're using a bar graph to display the probability distribution for the number of items a customer might select at a convenience store.

To construct a proper bar graph, follow these steps:

• Label the x-axis with the categorical variable, which in this case are the number of items (1 through 5).
• Label the y-axis with the probability values, ensuring the scale accommodates the probabilities given (up to 0.32).
• For each number of items, draw a bar whose height represents its probability: 0.32 for 1 item, 0.12 for 2 items, 0.23 for 3 items, 0.18 for 4 items, and 0.15 for 5 items.

Bar graphs make it easier to compare the probabilities of various outcomes at a glance. They serve as a visual complement to the probability table, providing another perspective that helps to solidify understanding.

The sum of probabilities is a critical concept in probability theory, stating that the total probability for all possible outcomes of a random experiment must equal 1. This principle ensures that all outcomes have been accounted for and confirms the validity of the probability distribution.

When dealing with the probability of selecting items at a convenience store, this translates to adding up the probabilities of selecting 1, 2, 3, 4, or 5 items: \[0.32 + 0.12 + 0.23 + 0.18 + 0.15 = 1.00\]Checking that the sum equals 1 is not only a mathematical necessity but also a good practice to verify the correctness of a probability distribution.

By ensuring the sum of probabilities is 1, we confirm that we have a complete and valid representation of all possible outcomes in the data set.