Question

Suppose that a recent poll of American households about car ownership found that for households with a car, 39% owned a sedan, 33% owned a van, and 7% owned a sports car. Suppose that three households are selected randomly and with replacement. What is the probability that at least one of the three randomly selected households own a sports car

Answer 1

Answer:

The probability that of the 3 households randomly selected at least 1 owns a sports car is 0.1956.

Step-by-step explanation:

Let X = number of household owns a sports car.

The probability of X is, P (X) = p = 0.07.

Then the random variable X follows a Binomial distribution with n = 3 and p = 0.07.

The probability function of a binomial distribution is:

$P(X=x) = {n\choose x}p^{x}[1-p]^{n-x}$

Compute the probability that of the 3 households randomly selected at least 1 owns a sports car:

$P(X\geq 1)=1-P(X$

Thus, the probability that of the 3 households randomly selected at least 1 owns a sports car is 0.1956.