To determine the probability that a randomly selected person from this survey is 8 to 12 years old, given that their favorite sport is baseball, we follow these steps:
1. Identify Key Values:
- Number of people aged 8 to 12 who like baseball: 10
- Total number of people who like baseball: 46
2. Calculate the Conditional Probability:
- The conditional probability [tex]\( P(A|B) \)[/tex] is given by the ratio of the number of favorable outcomes to the total number of outcomes in the given condition.
- Here, [tex]\( P(8 \text{ - } 12 \text{ yrs | Baseball}) = \frac{\text{Number of 8-12 years old who like baseball}}{\text{Total number of people who like baseball}} \)[/tex].
3. Perform the Calculation:
- Substituting the values: [tex]\( P(8 \text{ - } 12 \text{ yrs | Baseball}) = \frac{10}{46} \)[/tex].
4. Convert to Percentage:
- Multiply by 100 to convert the fraction to a percentage: [tex]\( \left( \frac{10}{46} \right) \times 100 \approx 21.73913043478261 \% \)[/tex].
5. Round to the Nearest Whole Number:
- The calculated percentage is approximately [tex]\( 21.73913043478261 \% \)[/tex]. Rounding this to the nearest whole number gives us [tex]\( 22 \% \)[/tex].
Therefore, the probability that a randomly selected person from this survey is 8 to 12 years old, given that their favorite sport is baseball, is [tex]\( \boxed{22\%} \)[/tex].
