Suppose that 56% of people own dogs. if you pick two people at random, what is the probability that they both own a dog?

The probability to one person to be a dog owner is p=0.56 (because 56% of people own dogs) and the probability that one person is not dog owner is q=1-p=1-0.56=0.44.
Choosing two people at random, there are such possibilities:

1. both are dog owners;
2. first owns a dog, second not;
3. first hasn't dog, second owns a dog;
4. both haven't dogs.

Let's count the probabilities for all these cases:
1. ;
2. ;
3. ;
4. .
Note that 0.3136+0.2464+0.2464+0.1936=1, this means that all possible cases were considered.
if you pick two people at random the probability that they both own a dog is 0.3136.