https://r2.erweima.ai/mathbot/image/17267015607148yvqqidf.jpg

Let's analyze the problem shown in the image step by step.

We are given a Venn diagram representing the friends of the bride ("Novia") and the groom ("Novio") at a wedding, as well as the number of friends that are exclusively friends of one, friends of both, or neither.

- **29** are friends of the bride only.
- **20** are friends of the groom only.
- **30** are friends of both the bride and the groom.
- **1** person is neither a friend of the bride nor the groom.

There are **80** total guests, and the problem asks for the conditional probability that a randomly selected friend of the groom is also a friend of the bride.

### Conditional Probability Formula
The formula for conditional probability is:
\[
P(A|B) = \frac{P(A \cap B)}{P(B)}
\]
Where:
- \(P(A|B)\) is the probability of event \(A\) (being a friend of the bride) given that event \(B\) (being a friend of the groom) has occurred.
- \(P(A \cap B)\) is the probability of being a friend of both the bride and groom.
- \(P(B)\) is the probability of being a friend of the groom.

### Step 1: Calculate \(P(A \cap B)\) and \(P(B)\)
- The number of people who are friends of both the bride and the groom is **30**, and the total number of guests is **80**.
  So, \(P(A \cap B) = \frac{30}{80}\).

- The number of people who are friends of the groom is **30 + 20 = 50** (those who are only friends of the groom plus those who are friends of both).
  So, \(P(B) = \frac{50}{80}\).

### Step 2: Apply the Formula
Now we can substitute these values into the conditional probability formula:
\[
P(\text{Friend of bride} | \text{Friend of groom}) = \frac{\frac{30}{80}}{\frac{50}{80}} = \frac{30}{50} = 0.6
\]

Thus, the probability that a randomly selected friend of the groom is also a friend of the bride is **0.6** or **60%**.

Let me know if you need further clarification or if you'd like more details!

Here are five related questions:
1. How would the result change if there were more people who were neither friends of the bride nor the groom?
2. What is the probability that a randomly selected guest is a friend of both the bride and the groom?
3. How would you calculate the probability that a randomly selected guest is a friend of the bride but not the groom?
4. Can you calculate the probability that a guest is not a friend of the bride nor the groom?
5. How does conditional probability differ from regular probability in this context?

**Tip:** Conditional probability helps isolate a specific condition, making it easier to focus on the likelihood of a second event happening based on the first event occurring.

Dado que un invitado seleccionado aleatoriamente es amigo del novio, encuentra la probabilidad de que sea amigo de la novia.

This problem involves finding the conditional probability that a randomly selected friend of the groom is also a friend of the bride, using a Venn diagram and set theory. Suitable for high school students learning about probability and statistics.

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