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Conditional Frequency 6C9D1E

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1. **State the problem:** We need to find the conditional relative frequency that a hiker has a backpack given that the hiker has a water bottle. 2. **Recall the formula for conditional relative frequency:** $$P(\text{Backpack} \mid \text{Water Bottle}) = \frac{P(\text{Backpack and Water Bottle})}{P(\text{Water Bottle})}$$ 3. **Identify values from the table:** - $P(\text{Backpack and Water Bottle}) = 0.59$ - $P(\text{Water Bottle}) = 0.8$ 4. **Calculate the conditional relative frequency:** $$P(\text{Backpack} \mid \text{Water Bottle}) = \frac{0.59}{0.8}$$ 5. **Show intermediate step with cancellation:** $$P(\text{Backpack} \mid \text{Water Bottle}) = \frac{\cancel{0.59}}{\cancel{0.8}} = 0.7375$$ 6. **Round to the nearest hundredth:** $$0.7375 \approx 0.74$$ 7. **Convert to percent:** $$0.74 \times 100 = 74\%$$ **Final answers:** - Decimal approximation: 0.74 - Percent approximation: 74%