To determine the probability that both of two randomly chosen people own a dog, given that 50% (or 0.5) of people own a dog, we can follow these steps:
1. Understand the given probability:
- The probability that a single person owns a dog is given, which is 50%, or 0.5.
2. Identify the event we are interested in:
- We want to find the probability that both of the two randomly chosen individuals own a dog.
3. Calculate the combined probability:
- Since the ownership of a dog by one person is independent of the ownership by another person, we can multiply the individual probabilities together to get the combined probability.
- The probability that the first person owns a dog is 0.5.
- The probability that the second person also owns a dog is 0.5.
- So, the probability that both people own a dog is [tex]\( 0.5 \times 0.5 \)[/tex].
4. Perform the multiplication:
- [tex]\( 0.5 \times 0.5 = 0.25 \)[/tex].
Therefore, the probability that both of the two randomly chosen people own a dog is 0.25.
