This is a probability problem related to the AND rule. Here's how to solve it:

Problem:

68% of people own dogs. What is the probability that two randomly selected people both own a dog?

Solution:

1. The probability that one person owns a dog is $P(\text{owns dog}) = 0.68$.

2. If we select two people independently (assuming their ownership is not linked), the probability that both own a dog is given by the formula: $P(\text{both own dogs}) = P(\text{person 1 owns dog}) \times P(\text{person 2 owns dog})$

3. Substituting $P(\text{owns dog}) = 0.68$: $P(\text{both own dogs}) = 0.68 \times 0.68$

4. Perform the calculation: $P(\text{both own dogs}) = 0.4624$

Final Answer:

The probability that both people own dogs is 0.462 (rounded to three decimal places).

Would you like a detailed breakdown of this calculation or assistance with similar problems?

Related Questions:

1. What is the probability that neither person owns a dog?
2. What is the probability that exactly one of the two people owns a dog?
3. How does the probability change if 80% of people own dogs instead of 68%?
4. How would the answer differ if owning a dog were not independent for the two people?
5. Can we calculate the probability using a fraction instead of a decimal?

Tip:

When working with probabilities, ensure you carefully consider whether events are independent or dependent, as this affects the calculation.