### Probability Problem and Solution Explanation#### Problem StatementA shipment of 30 computers has arrived at a store. The manufacturer of the computers called the store manager saying that 8 of the computers were defective. If the store has already sold 5 of these computers, what is the probability that at least two are defective?#### Solution ApproachTo solve this problem, we can use combinations to calculate the probabilities.1. **Define Combinations:** - Total computers = 30 - Defective computers = 8 - Computers sold = 52. **Calculate Probabilities:** We need to find the probability of at least two computers being defective out of the sold five. - **Compute Total Possible Combinations:** The total possible ways to select 5 computers from 30: \[ C(30, 5) = \frac{30!}{5!(30-5)!} \] - **Number of Ways to Choose 0 or 1 Defective Computer:** Calculate combinations for 0 defective: \[ C(22, 5) = \frac{22!}{5!(22-5)!} \] Calculate combinations for 1 defective: \[ C(8, 1) \cdot C(22, 4) = \frac{8!}{1!(8-1)!} \cdot \frac{22!}{4!(22-4)!} \] - **Use Complementary Probability:** Calculate probability of having 0 or 1 defective and subtract from 1: \[ P(\text{At least 2 defective}) = 1 - \left(\frac{C(22, 5) + C(8, 1) \cdot C(22, 4)}{C(30, 5)}\right) \]#### Graph and Diagram ExplanationThere is no graph or diagram provided in the image. The solution involves mathematical calculations using the concept of combinations in probability to solve the problem of defective computers.This approach highlights the importance of understanding combinations and probability theory for analyzing real-world situations in logistics and quality control.

2. A shipment of 30 computers has arrived at a store. The manufacturer of the computers called the store manager saying that 8 of the computers were defective. If the store has already sold 5 of these computers, what is the probability that at least two is defective?

2. A shipment of 30 computers has arrived at a store. The manufacturer of the computers called the store manager saying that 8 of the computers were defective. If the store has already sold 5 of these computers, what is the probability that at least two is defective?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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