Question

try it! use the test for independence

1. the table below shows the

vehicles in a parking garage
one afternoon. a vehicle in
the garage will be selected
at random. let r represent
\the vehicle is red\ and
c represent \the vehicle is a
car.\ are the events r and c
independent or dependent?
explain.

Explanation:

Step1: Calculate \(P(R)\)

The total number of vehicles is \(n = 22\). The number of red vehicles \(n(R)=7\). So \(P(R)=\frac{n(R)}{n}=\frac{7}{22}\)

Step2: Calculate \(P(C)\)

The number of cars \(n(C) = 11\). So \(P(C)=\frac{n(C)}{n}=\frac{11}{22}=\frac{1}{2}\)

Step3: Calculate \(P(R\cap C)\)

The number of red - cars \(n(R\cap C)=5\). So \(P(R\cap C)=\frac{n(R\cap C)}{n}=\frac{5}{22}\)

Step4: Check the independence condition \(P(R\cap C)=P(R)\times P(C)\)

Calculate \(P(R)\times P(C)=\frac{7}{22}\times\frac{1}{2}=\frac{7}{44}\approx0.159\) and \(P(R\cap C)=\frac{5}{22}\approx0.227\)

Since \(\frac{5}{22}
eq\frac{7}{44}\), the events \(R\) and \(C\) are not independent.

Answer:

The events \(R\) (the vehicle is red) and \(C\) (the vehicle is a car) are dependent.