https://file.aiquickdraw.com/mathbot/file/1730237539233xbg9yn2y.jpg

To solve this problem, let's go through it step-by-step.

### Problem Analysis
- A manufacturer shipped **50 cameras**, out of which **8 are defective**.
- The electronics store sold **15 cameras** without knowing which are defective.
- We are asked to find the probability that **at least one defective camera was sold**.

### Steps to Solution
To determine this probability, we can first calculate the probability that **no defective cameras** were sold and then subtract this from 1 to get the probability that **at least one defective camera** was sold.

1. **Total Ways to Choose 15 Cameras** (from 50):
   This is given by \( C(50, 15) \), where \( C(n, k) \) represents a combination or "n choose k".

2. **Ways to Choose 15 Cameras That Are All Non-Defective**:
   Since there are 8 defective cameras, there are \( 50 - 8 = 42 \) non-defective cameras. The number of ways to select 15 non-defective cameras from these 42 is \( C(42, 15) \).

3. **Probability of No Defective Cameras Being Sold**:
   This probability is the ratio of the ways to choose only non-defective cameras to the total ways of choosing 15 cameras:
   \[
   P(\text{no defective cameras sold}) = \frac{C(42, 15)}{C(50, 15)}
   \]

4. **Probability of At Least One Defective Camera Being Sold**:
   To find this, subtract the probability of no defective cameras from 1:
   \[
   P(\text{at least one defective camera sold}) = 1 - \frac{C(42, 15)}{C(50, 15)}
   \]

### Answer
Using the formula above will give the probability that at least one defective camera was sold.

Would you like the calculations for the exact values of \( C(42, 15) \) and \( C(50, 15) \), or do you have any other questions?

---

### Further Questions
1. How do combinations work, and how are they calculated?
2. What would change if we had more or fewer defective cameras?
3. Can you explain why we subtract from 1 to find the probability of "at least one defective"?
4. What is the general formula for solving similar probability problems involving "at least one"?
5. How does this method change if replacements were allowed when choosing items?

### Tip
In probability problems involving "at least one," it’s often easier to calculate the probability of the complement event ("none") and subtract it from 1.

A manufacturer has shipped 50 cameras to an electronics store, of which 8 are defective. If the electronics store sold 15 cameras before discovering that some were defective, what is the probability that at least one defective camera was sold?

Find the probability that an electronics store sold at least one defective camera from a shipment of 50 cameras, including 8 defective ones, by calculating the complementary probability of no defective cameras being sold. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation