It looks like you've uploaded a document containing several probability questions. Here’s a breakdown of the examples in the image you provided:

1. Example 4.1: Probability of getting a sum of 8 when rolling two dice.
2. Example 4.2: Conditional probability regarding the color of a second marble selected, given the first one was red.
3. Example 4.3: Conditional probability in a family with two children, given one is a boy.
4. Example 4.4: Bayesian probability problem about the accuracy of an HIV test and its false positives/negatives.
5. Example 4.5: Conditional probability involving families with dogs and cats.
6. Example 4.6: Probability of a person being a woman, given they received an A on a test in a class where a certain percentage of women and men received A's.

Would you like detailed solutions to any of these examples, or do you have a specific question on one of them? Let me know!

Here are five related questions to explore further:

1. How do you calculate conditional probabilities in examples like Example 4.2 and Example 4.3?
2. What is Bayes' Theorem, and how does it apply to Example 4.4?
3. What are common ways to approach probability problems involving dice, such as Example 4.1?
4. How do you solve probability problems when events are dependent, like in Example 4.5?
5. How would you apply the law of total probability to problems involving multiple conditions like in Example 4.6?

Tip: Always double-check if the events in your probability question are independent or dependent, as this affects how you calculate the probability.