A university class has 21 students: 11 are nursing majors, 4 are art majors, and 6 are psychology 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 nursing major and the second student is a psychology major?

Do not round your intermediate computations. Round your final answer to three decimal places.

To find the probability that the first student selected is a nursing major and the second student is a psychology major, we need to follow these steps:

### Step 1: Calculate the total number of students.
The total number of students is:
\[
21
\]

### Step 2: Calculate the probability that the first student selected is a nursing major.
There are 11 nursing majors out of 21 students, so the probability that the first student selected is a nursing major is:
\[
\frac{11}{21}
\]

### Step 3: Calculate the probability that the second student selected is a psychology major.
After the first student is selected (and assuming the first student was a nursing major), there are 20 students left, of which 6 are psychology majors. Therefore, the probability that the second student selected is a psychology major is:
\[
\frac{6}{20} = \frac{3}{10}
\]

### Step 4: Calculate the combined probability.
Since the selection of the first and second students are independent events, the combined probability is the product of the two individual probabilities:
\[
\text{Probability} = \frac{11}{21} \times \frac{3}{10} = \frac{33}{210}
\]

### Step 5: Simplify and round the final answer.
The fraction \(\frac{33}{210}\) simplifies to:
\[
\frac{11}{70} \approx 0.157
\]

Thus, the probability that the first student selected is a nursing major and the second student is a psychology major is approximately **0.157**.

Would you like more details or have any questions?

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Here are 8 related questions to consider:

1. What is the probability that the first student selected is a psychology major and the second is an art major?
2. How does the probability change if the class size increases to 25 with the same proportions of majors?
3. What is the probability that both selected students are nursing majors?
4. If three students are selected one after the other, what is the probability that they are from three different majors?
5. What is the probability that neither of the selected students is a psychology major?
6. How does the order of selection affect the overall probability in this scenario?
7. What is the probability that the second student selected is a nursing major given that the first student was not a nursing major?
8. How would the probabilities change if the number of art majors doubled?

**Tip:** In probability problems involving multiple selections without replacement, always adjust the total number of possible outcomes for the second event.

Calculate the probability that the first student selected in a university class is a nursing major and the second student is a psychology major. Follow a step-by-step solution using probability theory, considering independent events. Suitable for Grades 9-12.

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