Question

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

what is the probability that a randomly selected person from this surveys favorite sport is football, given they are 8 to 12 years old?

\\(p(\text{football} \mid 8 - 12\text{ yrs}) = \quad\\%\\)

round your answer to the nearest whole percent.

Explanation:

Identify the given condition and target group

$$ \text{Condition: } 8 - 12\text{ yrs} $$

$$ \text{Total in } 8 - 12\text{ yrs group} = 23 + 13 + 7 = 43 $$

Calculate the conditional probability

$$ \text{Number whose favorite sport is Football in } 8 - 12\text{ yrs group} = 23 $$

$$ P(\text{Football} \mid 8 - 12\text{ yrs}) = \frac{23}{43} \approx 0.53488 $$

Convert to percentage and round

$$ 0.53488 \times 100\% \approx 53.49\% \approx 53\% $$

Answer:

What is the probability that a randomly selected person from this survey's favorite sport is football, given they are 8 to 12 years old?

\(P(\text{Football} \mid 8 - 12\text{ yrs}) =\) <blank>53</blank>%