Final answer:
The probability that the tenth person randomly interviewed is the fifth one to own a dog is approximately 0.1029.
Step-by-step explanation:
The probability that the tenth person randomly interviewed is the fifth one to own a dog can be calculated using the formula for the probability of independent events. We can assume that each person interviewed is independent of each other, and the probability of each person owning a dog is 0.3. To find the probability that the tenth person is the fifth one to own a dog, we can use the binomial probability formula:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
where P(X=k) is the probability of getting exactly k successes, n is the number of trials, p is the probability of success, and C(n, k) is the binomial coefficient. In this case, we have n=10, k=5, and p=0.3. Plugging in these values into the formula, we get:
P(X=5) = C(10, 5) * 0.3^5 * (1-0.3)^(10-5)
Simplifying this expression, we get:
P(X=5) = 252 * 0.3^5 * 0.7^5
Computing this expression, we find that the probability that the tenth person randomly interviewed is the fifth one to own a dog is approximately 0.10291936.