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:
[tex]P(X=x) = {n\choose x}p^{x}[1-p]^{n-x}\\[/tex]
Compute the probability that of the 3 households randomly selected at least 1 owns a sports car:
[tex]P(X\geq 1)=1-P(X<1)\\=1-P(X=0)\\=1- {3\choose 0}(0.07)^{0}[1-0.07]^{3-0}\\=1-0.8044\\=0.1956[/tex]
Thus, the probability that of the 3 households randomly selected at least 1 owns a sports car is 0.1956.
