Subjects statistics

Conditional Probability 35Eddc

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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%**.