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Suppose that 66% of people own dogs. if you pick two people at random, what is the probability that they both own a dog?

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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%.

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