The probability all three of the students have the same major is 0.0909.
The probability that at least one of the three students is an engineering major is 0.7613.
The probability that either all of the three students are psychology majors or none of the students are psychology majors is 0.0909.
Based on the calculations, here are the probabilities for the given scenarios, accurate to four decimal places:
1. Probability that all three of the students have the same major:
- This probability is approximately 0.0909.
2. Probability that at least one of the three students is an engineering major:
- This probability is approximately 0.7613.
3. Probability that either all of the three students are psychology majors or none of the students are psychology majors:
- This probability is also approximately 0.0909.
These probabilities are calculated based on the combination formula, considering the total number of students in each major and the total number of students overall.