https://r2.erweima.ai/mathbot/image/1726142023808qe2rr3yp.jpg

The image contains a probability-related problem written in Chinese. Here is a translated version of the text:

---
3. A shop stores multiple boxes containing glass cups. Each box contains 20 cups. Among the cups in a box, a customer randomly selects 4 cups for inspection, and the result shows that there are 0, 1, or 2 defective cups. The probabilities of the box containing 0, 1, or 2 defective cups are respectively 0.8, 0.1, and 0.1. Given that a customer buys this box, what is the probability that the box contains a defective cup?

---

This is a typical problem involving conditional probability, where we need to calculate the probability that the box contains defective cups based on the given probabilities.

Let me know if you'd like me to solve the problem or provide further details.

Here are some related questions to expand on this concept:

1. What is Bayes' Theorem, and how can it help solve probability problems?
2. How do you calculate the expected number of defective items in a box?
3. What is the difference between independent and conditional probability?
4. How can the law of total probability be applied in this situation?
5. How can we generalize this problem if the number of defective cups is greater than 2?

**Tip:** Conditional probability is often calculated using Bayes' Theorem, which allows you to reverse conditional dependencies by knowing prior probabilities and evidence.

A shop stores multiple boxes containing glass cups. Each box contains 20 cups. Among the cups in a box, a customer randomly selects 4 cups for inspection, and the result shows that there are 0, 1, or 2 defective cups. The probabilities of the box containing 0, 1, or 2 defective cups are respectively 0.8, 0.1, and 0.1. Given that a customer buys this box, what is the probability that the box contains a defective cup?

Solve a real-world conditional probability problem involving defective cups in a box. Learn how to apply Bayes' Theorem and the law of total probability to determine the likelihood of purchasing a box with defective cups. Suitable for high school students and beyond.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation