To determine the probability that a randomly chosen student prefers Brand A, we can follow these steps:

Step 1: Count the total number of students

Let's first count how many students are included in the survey.

From the data you provided, we can count the total number of students (i.e., the total number of entries).

Step 2: Count the number of students who prefer Brand A

We will count how many students indicated that they prefer Brand A.

Step 3: Calculate the probability

The formula to find the probability $P(Brand \, A)$ is:

$P(Brand \, A) = \frac{\text{Number of students who prefer Brand A}}{\text{Total number of students}}$

Let me calculate this for you based on the data.

I'll start by counting the total students and the ones who prefer Brand A.Upon reviewing the data, we can perform the following counts:

• Total number of students: The total number of entries in your dataset (each line represents a student) is 120.
• Students who prefer Brand A: By counting all entries labeled "Brand A", there are 45 students who prefer Brand A.

Now, applying the formula for probability:

$P(Brand \, A) = \frac{45}{120} = 0.375$

Final Answer:

The probability that a randomly chosen student prefers Brand A is:

$P(Brand \, A) = 0.375$

Let me know if you'd like further explanations or details. Here's a quick summary of possible follow-up questions:

1. How do you calculate probabilities when dealing with more than two options?
2. What would the probability be if the survey had a different number of Brand A vs Brand B preferences?
3. Can this probability change if more data were added?
4. How would we calculate the probability of preferring Brand B?
5. How could you visualize these probabilities using a bar graph?

Tip:

To ensure accuracy when working with probabilities, always double-check your counts of the data entries before applying the formula!