a survey is conducted to study the favorite sport of individuals in different age groups. the two - way…

a survey is conducted to study the favorite sport of individuals in different age groups. the two - way table is given below:\n| | football | basketball | baseball | total |\n| 8 - 12 yrs | 10 | 12 | 10 | 32 |\n| 13 - 17 yrs | 8 | 6 | 24 | 38 |\n| 18 - 22 yrs | 16 | 2 | 12 | 30 |\n| total | 34 | 20 | 46 | 100 |\nwhat is the probability that a randomly selected person from this surveys favorite sport is basketball, given they are 18 to 22 years old?\np(basketball | 18 - 22 yrs) = ?%\nround your answer to the nearest whole percent.

a survey is conducted to study the favorite sport of individuals in different age groups. the two - way table is given below:\n| | football | basketball | baseball | total |\n| 8 - 12 yrs | 10 | 12 | 10 | 32 |\n| 13 - 17 yrs | 8 | 6 | 24 | 38 |\n| 18 - 22 yrs | 16 | 2 | 12 | 30 |\n| total | 34 | 20 | 46 | 100 |\nwhat is the probability that a randomly selected person from this surveys favorite sport is basketball, given they are 18 to 22 years old?\np(basketball | 18 - 22 yrs) = ?%\nround your answer to the nearest whole percent.

Answer

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of the table, $P(\text{Basketball}|18 - 22\text{ yrs})=\frac{\text{Number of 18 - 22 yr - olds who like basketball}}{\text{Total number of 18 - 22 yr - olds}}$.

Step2: Identify values from the table

The number of 18 - 22 yr - olds who like basketball is 2, and the total number of 18 - 22 yr - olds is 30.

Step3: Calculate the probability

$P(\text{Basketball}|18 - 22\text{ yrs})=\frac{2}{30}=\frac{1}{15}\approx 0.0667$.

Step4: Convert to percentage

To convert the decimal to a percentage, multiply by 100. So $0.0667\times100 = 6.67%$. Rounding to the nearest whole percent gives 7%.

Answer:

7%