A university class has 21 students: 11 are psychology majors, 4 are business majors, and 6 are art majors. (Each student has only one of these majors.) The professor is planning to select two of the students for a demonstration. The first student will be selected at random, and then the second student will be selected at random from the remaining students. What is the probability that the first student selected is a business major and the second student is an art major?
Do not round your intermediate computations. Round your final answer to three decimal places.

To solve the problem, we need to calculate the probability that:

1. The first student selected is a business major.
2. The second student selected is an art major.

### Step-by-Step Solution:

#### Total number of students:
The total number of students is 21.

#### Step 1: Probability that the first student is a business major:
There are 4 business majors out of 21 total students. So, the probability that the first student selected is a business major is:

\[
P(\text{first is business major}) = \frac{4}{21}
\]

#### Step 2: Probability that the second student is an art major:
After selecting a business major, there are 20 students left, and 6 of those remaining students are art majors. So, the probability that the second student selected is an art major is:

\[
P(\text{second is art major}) = \frac{6}{20}
\]

#### Step 3: Calculate the combined probability:
Since these are independent events (the selection of the second student depends on the first but is still random within the remaining group), we multiply the probabilities:

\[
P(\text{first business, second art}) = \frac{4}{21} \times \frac{6}{20}
\]

Let's compute this:

\[
P(\text{first business, second art}) = \frac{4 \times 6}{21 \times 20} = \frac{24}{420} = \frac{2}{35}
\]

#### Step 4: Final answer:
Now, we convert this to a decimal by dividing \( \frac{2}{35} \):

\[
\frac{2}{35} = 0.0571
\]

Thus, the probability that the first student selected is a business major and the second student is an art major is approximately **0.057** (rounded to three decimal places).

### Final Answer:
\[
P(\text{first business, second art}) = 0.057
\]

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions:
1. What is the probability that both students selected are business majors?
2. What is the probability that both students selected are art majors?
3. How would the probability change if there were an equal number of students from each major?
4. What is the probability that the first student selected is an art major and the second is a psychology major?
5. What is the probability that the second student selected is a business major, regardless of the first selection?

**Tip**: When dealing with successive events in probability, always remember to update the total number of outcomes after each selection!

A university class has 21 students: 11 are psychology majors, 4 are business majors, and 6 are art majors. (Each student has only one of these majors.) The professor is planning to select two of the students for a demonstration. The first student will be selected at random, and then the second student will be selected at random from the remaining students. What is the probability that the first student selected is a business major and the second student is an art major? Do not round your intermediate computations. Round your final answer to three decimal places.

Calculate the probability of selecting a business major first and an art major second in a class of 21 students, using key probability concepts. Follow a detailed step-by-step solution and learn how to handle dependent events and probability fractions. Perfect for high school students in Grades 10-12.

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