A survey is conducted to study the favorite sport of individuals in different age groups. The two-way table is given below:

| Age Group | Football | Basketball | Baseball | Total |
|---------------|----------|------------|----------|-------|
| 8-12 years | 10 | 12 | 10 | 32 |
| 13-17 years | 8 | 6 | 24 | 38 |
| 18-22 years | 16 | 2 | 12 | 30 |
| Total | 34 | 20 | 46 | 100|

What is the probability that a randomly selected person from this survey is 8 to 12 years old, given their favorite sport is baseball?

[tex]\[ P(8-12 \text{ yrs | Baseball}) = \, [?] \% \][/tex]

Round your answer to the nearest whole percent.



Answer :

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].