# Probability Calculation Based on Inspection Data Let's solve each part step by step using the data provided. ## Data Table | Supplier | Functional | Faulty | |------------|------------|--------| | Supplier A | 180 | 20 | | Supplier B | 250 | 30 | | Supplier C | 100 | 20 | **Total microchips:** \( 180+20+250+30+100+20 = \textbf{600} \) --- ## (a) Probability of Randomly Selecting a Microchip from Supplier C Number of microchips from Supplier C: \( 100 + 20 = 120 \) \[ P(\text{Supplier C}) = \frac{120}{600} = \frac{1}{5} = 0.2 \] --- ## (b) Probability of Receiving a Faulty Microchip Total faulty microchips: \( 20 + 30 + 20 = 70 \) \[ P(\text{Faulty}) = \frac{70}{600} = \frac{7}{60} \approx 0.117 \] --- ## (c) Probability a Microchip is Functional Given It Was Supplied by Company A Number of microchips from Supplier A: \( 180 + 20 = 200 \) Number functional from Supplier A: \( 180 \) \[ P(\text{Functional} \mid \text{Supplier A}) = \frac{180}{200} = 0.9 \] --- ## (d) Mutually Exclusive Events **Event 1:** Microchip is from Supplier B **Event 2:** Microchip is faulty - Mutually exclusive events cannot happen together. - A microchip from Supplier B **can** be faulty (there are 30 such microchips). **Answer:** No, these events are **not mutually exclusive** because there are microchips that are both from Supplier B and faulty (30 such microchips). --- ## **Summary Table** | Part | Probability/Explanation | |------|------------------------| | (a) | \(0.2\) | | (b) | \(0.117\) | | (c) | \(0.9\) | | (d) | **Not mutually exclusive (can occur together)** | --- **Let me know if you need step-by-step calculations for any part!**