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, follow these steps:
1. Identify the relevant values from the provided table.
- The number of individuals whose favorite sport is basketball in the 18 to 22 years age group: [tex]\( 2 \)[/tex]
- The total number of individuals in the 18 to 22 years age group: [tex]\( 30 \)[/tex]
2. Calculate the conditional probability.
The conditional probability formula is:
[tex]\[
P(\text{Basketball} \mid \text{18-22 yrs}) = \frac{\text{Number of individuals whose favorite sport is basketball in 18-22 yrs}}{\text{Total number of individuals in 18-22 yrs}}
\][/tex]
Substitute the identified values:
[tex]\[
P(\text{Basketball} \mid \text{18-22 yrs}) = \frac{2}{30}
\][/tex]
3. Convert the probability to a percentage.
[tex]\[
P(\text{Basketball} \mid \text{18-22 yrs}) = \left(\frac{2}{30}\right) \times 100 \%
\][/tex]
4. Perform the calculation.
[tex]\[
P(\text{Basketball} \mid \text{18-22 yrs}) = 6.66666666667 \%
\][/tex]
5. Round to the nearest whole percent.
[tex]\[
P(\text{Basketball} \mid \text{18-22 yrs}) \approx 7 \%
\][/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].
