A university class has 

29

 students: 

14

 are psychology majors, 

9

 are accounting majors, and 

6

 are history 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 psychology major and the second student is an accounting major?

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

(If necessary, consult a list of formulas.)

To determine the probability that the first student selected is a psychology major and the second student is an accounting major, we can break the problem down into two steps:

### Step 1: Probability that the first student is a psychology major

The number of psychology majors is 14, and the total number of students is 29. So, the probability that the first student selected is a psychology major is:

\[
P(\text{first psychology major}) = \frac{14}{29}
\]

### Step 2: Probability that the second student is an accounting major given that the first student was a psychology major

If the first student selected was a psychology major, there are now 28 students left, with 9 accounting majors still remaining. Therefore, the probability that the second student selected is an accounting major given that the first was a psychology major is:

\[
P(\text{second accounting major} \mid \text{first psychology major}) = \frac{9}{28}
\]

### Step 3: Combined Probability

The probability of both events occurring (selecting a psychology major first and then an accounting major second) is the product of the two probabilities:

\[
P(\text{psychology major first and accounting major second}) = \frac{14}{29} \times \frac{9}{28}
\]

Now, let's compute the product:

\[
P(\text{psychology major first and accounting major second}) = \frac{14 \times 9}{29 \times 28} = \frac{126}{812}
\]

Now, divide the fraction:

\[
P(\text{psychology major first and accounting major second}) = \frac{126}{812} \approx 0.155
\]

### Final Answer:
The probability that the first student selected is a psychology major and the second student is an accounting major is approximately **0.155** (rounded to three decimal places).

Do you have any questions or would you like more details?

Here are some related questions:
1. What is the probability that the first student selected is an accounting major and the second is a history major?
2. What is the probability that both selected students are psychology majors?
3. What is the probability that neither of the selected students is a psychology major?
4. What is the probability that the second student selected is a history major, regardless of the first student's major?
5. How does the probability change if the professor selects three students instead of two?

**Tip:** When calculating probabilities for multiple sequential events, it's essential to consider the impact of each event on the subsequent possibilities, especially when dealing with selection without replacement.

Explore the probability of selecting a psychology major first and an accounting major second among 29 students with specific majors. Detailed solution and calculations provided.

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