Probability can be really tricky, especially for students who are seeing it for the first time in university statistics classes. Here are some important ideas that can make it difficult:

1. Understanding Events and Sample Spaces:
   It can be confusing to define events and their sample spaces. Many students find it hard to picture all the possible outcomes. This can lead to mistakes when calculating probability.

2. Conditional Probability:
   Understanding whether events affect each other makes things more complicated. The formula for conditional probability, $P(A|B) = \frac{P(A \cap B)}{P(B)}$, is often used incorrectly, which can lead to wrong answers.

3. The Law of Large Numbers:
   This rule says that as you do more trials, the average result will get closer to the expected value. This can be surprising for students. They might not see how small samples can seem random.

4. Bayes’ Theorem:
   This theorem talks about using prior probabilities, but is often misunderstood. The formula $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$ needs careful use of probabilities, which can be tricky.

Solutions:

• Practice and Visualization: Doing regular exercises and using visual aids can help make these ideas clearer.
• Collaborative Learning: Studying in groups allows students to discuss and explain things to each other, which can improve understanding.
• Seek Help: Getting support from tutors or using online resources can provide the extra help needed.

It’s important to tackle these challenges to really understand probability in statistics.