To determine the probability that a randomly selected person from the survey owns a dog given that they are a senior citizen, we need to assess the relevant data and follow these steps:
1. Identify the number of senior citizens who own a dog: From the given table, we see that 22 senior citizens own a dog.
2. Identify the total number of senior citizens surveyed: The table shows that there are 30 senior citizens in total.
3. Compute the conditional probability: The probability that a person owns a dog given that they are a senior citizen is calculated by dividing the number of senior citizens who own a dog by the total number of senior citizens:
[tex]\[
P(\text{Dog} \mid \text{Senior Citizen}) = \frac{\text{Number of senior citizens with a dog}}{\text{Total number of senior citizens}} = \frac{22}{30}
\][/tex]
4. Convert the probability to a percentage: Multiplying the probability by 100 to convert it to a percentage:
[tex]\[
P(\text{Dog} \mid \text{Senior Citizen}) \times 100 = \left(\frac{22}{30}\right) \times 100 \approx 73.33\%
\][/tex]
5. Round to the nearest whole percent: The final step is to round 73.33% to the nearest whole number, which is 73%.
Thus, the probability that a randomly selected person from this survey owns a dog given that they are a senior citizen is:
[tex]\[
P(\text{Dog} \mid \text{Senior Citizen}) = 73\%
\][/tex]
