Final answer:
The probability of two people owning a dog when 66% of people own dogs is found by squaring the probability (0.66), giving us a result of 0.4356 or 43.56%.
Step-by-step explanation:
The question asks to calculate the probability that both people picked at random own a dog when it is known that 66% of people own dogs. To find this probability, we can simply multiply the probability of the first person owning a dog by the probability of the second person owning a dog, assuming that these events are independent.
The probability that one person owns a dog is given as 66%, which is 0.66 in decimal form. Thus, the probability that both people own a dog is 0.66 × 0.66 (or 0.66 squared). Calculation yields:
0.66 × 0.66 = 0.4356
Therefore, the probability that both people own a dog is 0.4356, or 43.56%.