1. **State the problem:** We want to find the probability that a randomly selected person is from the South given that their favorite dessert is ice cream. This is a conditional probability problem.
2. **Formula:** The conditional probability formula is:
$$P(\text{South} \mid \text{Ice Cream}) = \frac{P(\text{South and Ice Cream})}{P(\text{Ice Cream})}$$
3. **Identify values from the table:**
- Number of people from South who like Ice Cream = 16
- Total number of people who like Ice Cream = 30
4. **Calculate the probability:**
$$P(\text{South} \mid \text{Ice Cream}) = \frac{16}{30}$$
5. **Simplify the fraction:**
$$\frac{16}{30} = \frac{\cancel{2} \times 8}{\cancel{2} \times 15} = \frac{8}{15}$$
6. **Convert to percentage:**
$$\frac{8}{15} \approx 0.5333 = 53.33\%$$
7. **Round to nearest whole percent:**
$$53\%$$
**Final answer:** The probability that a randomly selected person is from the South given their favorite dessert is ice cream is **53%**.
Conditional Probability 35Eddc
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