Questions: A marketing survey compiled data on the number of cars in households. If X= the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the following probability distribution: X 012345 P(X) 0.240 .370 .200 .110 .050 .03 What is the probability that a randomly chosen household has at least two cars?

Solution Steps

To find the probability that a randomly chosen household has at least two cars, we need to calculate the sum of the probabilities of having 2, 3, 4, or 5 cars. This can be done by adding the probabilities associated with these outcomes.

The probability distribution for the number of cars \( X \) in a randomly selected household is given as follows:

\[ \begin{array}{c|c} X & P(X) \\ \hline 0 & 0.240 \\ 1 & 0.370 \\ 2 & 0.200 \\ 3 & 0.110 \\ 4 & 0.050 \\ 5 & 0.030 \\ \end{array} \]

To find the probability that a randomly chosen household has at least two cars, we need to sum the probabilities for \( X = 2, 3, 4, \) and \( 5 \):

\[ P(X \geq 2) = P(2) + P(3) + P(4) + P(5) \]

Substituting the values from the distribution:

\[ P(X \geq 2) = 0.200 + 0.110 + 0.050 + 0.030 \]

Calculating the sum:

\[ P(X \geq 2) = 0.200 + 0.110 + 0.050 + 0.030 = 0.390 \]

Final Answer