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. [tex]p\cdot p=0.56\cdot 0.56=0.3136[/tex];
2. [tex]p\cdot q=0.56\cdot 0.44=0.2464[/tex];
3. [tex]q\cdot p=0.44\cdot 0.56=0.2464[/tex];
4. [tex]q\cdot q=0.44\cdot 0.44=0.1936[/tex].
Note that 0.3136+0.2464+0.2464+0.1936=1, this means that all possible cases were considered.
Answer: if you pick two people at random the probability that they both own a dog is 0.3136.
