https://file.aiquickdraw.com/mathbot/file/1726421406805y9jvzvrn.jpg

Let's analyze the data from the table in the image step by step to solve the probability questions. 

### The Table Breakdown:
The table gives us the number of shipments based on three factors:
- **Customs Cleared (H)** or **Customs Not Cleared (I)**
- **On-time Delivery (F)** or **Not On-time Delivery (G)**
- **Weather Disruption (J)**

We are given totals as well, and the overall total number of shipments is 300.

#### Questions:
1. **Shipment has Customs Clearance and On-time Delivery:**
   - The number of shipments with **Customs Cleared (H)** and **On-time Delivery (F)** is 110.
   - The total number of shipments is 300.
   - Probability = \( \frac{110}{300} \)

2. **Shipment does not have Customs Clearance:**
   - The total number of shipments that did **not** clear customs (Customs Not Cleared, I) is 80.
   - Probability = \( \frac{80}{300} \)

3. **Shipment either has Not On-time Delivery or experiences a Weather Disruption:**
   - Not On-time Delivery (G): 120 shipments.
   - Weather Disruption (J): 60 shipments.
   - However, 30 shipments overlap (those that are both Not On-time and affected by Weather Disruption).
   - Probability = \( \frac{120 + 60 - 30}{300} = \frac{150}{300} \)

4. **Shipment Neither Customs Clearance nor experiences a Weather Disruption:**
   - To calculate this, we consider those without Customs Clearance (Customs Not Cleared, I) **and** who do **not** experience Weather Disruption (i.e., 80 total not cleared - 30 with weather disruption = 50).
   - Probability = \( \frac{50}{300} \)

### Final Calculations:
- **P(Customs Cleared and On-time Delivery)** = \( \frac{110}{300} = 0.367 \)
- **P(Does not have Customs Clearance)** = \( \frac{80}{300} = 0.267 \)
- **P(Not On-time Delivery or Weather Disruption)** = \( \frac{150}{300} = 0.500 \)
- **P(Neither Customs Cleared nor Weather Disruption)** = \( \frac{50}{300} = 0.167 \)

Let me know if you'd like further clarification on any of these steps or additional details!

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Here are 5 questions to explore further:
1. How do we calculate probabilities when two events are mutually exclusive?
2. What is the meaning of "conditional probability" in real-world cases?
3. How can overlapping probabilities be handled with inclusion-exclusion principles?
4. Can the sum of all probabilities in this table equal more than 1? Why or why not?
5. How could weather disruptions affect delivery efficiency statistically?

**Tip**: Always check if events overlap when calculating the probability of union (either/or) events.

A shipping company has 300 shipments scheduled. Calculate the following probabilities: 1. Shipment has Customs Clearance and On-time Delivery. 2. Shipment does not have Customs Clearance. 3. Shipment either has Not On-time Delivery or experiences a Weather Disruption. 4. Shipment Neither Customs Clearance nor experiences a Weather Disruption.

Learn how to calculate probabilities for a shipping company's 300 scheduled shipments. This example explores events such as customs clearance, on-time delivery, and weather disruptions. Suitable for students in Grades 10-12.

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