Answer :
To solve the problem of finding the probability that a randomly selected person from the survey is aged 13 to 17 years, given that their favorite sport is football, we will follow these steps:
1. Identify the total number of individuals whose favorite sport is football:
According to the table, the total number of people who prefer football is given in the "Total" row under the "Football" column. This number is 34.
2. Determine the number of individuals aged 13 to 17 years who prefer football:
From the table, we can see the number of people aged 13 to 17 years whose favorite sport is football is specifically listed in the intersection of the "13 - 17 yrs" row and the "Football" column. This number is 8.
3. Calculate the conditional probability:
The probability that a person is 13 to 17 years old given that their favorite sport is football (denoted as [tex]\( P(13-17 \text{ yrs } \mid \text{ Football }) \)[/tex]) is calculated by dividing the number of people aged 13 to 17 who like football by the total number of people who like football.
[tex]\[ P(13-17 \text{ yrs } \mid \text{ Football }) = \frac{\text{Number of people aged 13 to 17 who like football}}{\text{Total number of people who like football}} \][/tex]
Plugging in the numbers:
[tex]\[ P(13-17 \text{ yrs. } \mid \text{ Football }) = \frac{8}{34} \][/tex]
4. Convert the fraction to a percentage:
To find the percentage, multiply the result by 100.
[tex]\[ P(13-17 \text{ yrs. } \mid \text{ Football }) \times 100 = \left(\frac{8}{34}\right) \times 100 \approx 23.52941176470588\% \][/tex]
5. Round to the nearest whole percent:
Finally, round 23.52941176470588 to the nearest whole number, which is 24%.
So, the probability that a randomly selected person from this survey is aged 13 to 17 years, given that their favorite sport is football, is approximately:
[tex]\[ 24\% \][/tex]
1. Identify the total number of individuals whose favorite sport is football:
According to the table, the total number of people who prefer football is given in the "Total" row under the "Football" column. This number is 34.
2. Determine the number of individuals aged 13 to 17 years who prefer football:
From the table, we can see the number of people aged 13 to 17 years whose favorite sport is football is specifically listed in the intersection of the "13 - 17 yrs" row and the "Football" column. This number is 8.
3. Calculate the conditional probability:
The probability that a person is 13 to 17 years old given that their favorite sport is football (denoted as [tex]\( P(13-17 \text{ yrs } \mid \text{ Football }) \)[/tex]) is calculated by dividing the number of people aged 13 to 17 who like football by the total number of people who like football.
[tex]\[ P(13-17 \text{ yrs } \mid \text{ Football }) = \frac{\text{Number of people aged 13 to 17 who like football}}{\text{Total number of people who like football}} \][/tex]
Plugging in the numbers:
[tex]\[ P(13-17 \text{ yrs. } \mid \text{ Football }) = \frac{8}{34} \][/tex]
4. Convert the fraction to a percentage:
To find the percentage, multiply the result by 100.
[tex]\[ P(13-17 \text{ yrs. } \mid \text{ Football }) \times 100 = \left(\frac{8}{34}\right) \times 100 \approx 23.52941176470588\% \][/tex]
5. Round to the nearest whole percent:
Finally, round 23.52941176470588 to the nearest whole number, which is 24%.
So, the probability that a randomly selected person from this survey is aged 13 to 17 years, given that their favorite sport is football, is approximately:
[tex]\[ 24\% \][/tex]
