It seems like you're working with a scenario that involves probability and statistics, specifically binomial probability, but I'll need more details to proceed. From the information you've provided, it seems a random sample of freshmen is selected, and we know the proportion planning to major in a STEM discipline. To move forward, I need to know:

1. The percentage or probability of freshmen planning to major in STEM.
2. The number of freshmen in the sample.

Could you provide these missing details? Once I have that, I can help calculate probabilities or expected values related to the problem.

Let me know if you have any questions!

Five related questions:

1. How do we compute binomial probabilities in a scenario like this?
2. What does the standard deviation of a binomial distribution represent in STEM-related data?
3. What are some real-world applications of binomial probability in education?
4. How would increasing the sample size affect the outcomes of the study?
5. What role does statistical significance play in STEM research results?

Tip: When working with binomial distributions, always check if you can use a normal approximation to simplify calculations if $n$ is large enough!