To determine the probability that a randomly selected person from this survey's favorite sport is basketball, given they are 18 to 22 years old (denoted as [tex]\( P(\text{Basketball} \mid 18-22 \text{ yrs}) \)[/tex]), we can follow these steps:
1. Identify the total number of people aged 18 to 22:
According to the table, there are 30 people in the age range of 18 to 22 years.
2. Identify the number of people aged 18 to 22 who prefer basketball:
From the table, 2 people in the age range of 18 to 22 years said that basketball is their favorite sport.
3. Calculate the probability:
The conditional probability [tex]\( P(\text{Basketball} \mid 18-22 \text{ yrs}) \)[/tex] is given by:
[tex]\[
P(\text{Basketball} \mid 18-22 \text{ yrs}) = \frac{\text{Number of people aged 18 to 22 who prefer basketball}}{\text{Total number of people aged 18 to 22}}
\][/tex]
Substituting the known values:
[tex]\[
P(\text{Basketball} \mid 18-22 \text{ yrs}) = \frac{2}{30}
\][/tex]
4. Convert the fraction to a percentage:
[tex]\[
\frac{2}{30} \times 100 = 6.666666666666667\%
\][/tex]
5. Round the result to the nearest whole percent:
[tex]\[
6.666666666666667\% \approx 7\%
\][/tex]
Therefore, the probability that a randomly selected person from this survey's favorite sport is basketball, given they are 18 to 22 years old, is approximately [tex]\( 7\% \)[/tex].
