The probability that the eleventh person randomly interviewed in the city is the eighth one to own a dog can be calculated using the binomial probability formula.
In this scenario:
- n is the total number of people interviewed (11).
- k is the number of people who own a dog before the eleventh person (7, since we want the eighth person to own a dog).
- p is the probability that a person owns a dog (0.35).
Using the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
P(X = 7) = (11 choose 7) * (0.35)^7 * (1-0.35)^(11-7)
You can calculate this probability by substituting the values into the formula.