Question

Forty-eight percent of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, $55\%$prefer life in prison without parole over the death penalty for a person convicted of first degree murder. $37.6\%$of all Californians are Latino. In this problem, let: • C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. L = Latino Californians. Suppose that one Californian is randomly selected.

Are L and C independent events? Show why or why not.

Short answer

No, L and C are not independent.

Step-by-step solution

Content Introduction

There are two events,

C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder.

L = Latino Californians.

Given that,

$$\begin{gathered} P\left(C\right)=0.48 \\ P\left(L\right)=0.376 \end{gathered}$$

Content Explanation

To prove two events independent of each other, justify the following given conditions:

$$\begin{gathered} 1.P\left(C\right|L)=P(C) \\ 2.P(L\left|C\right)=P\left(L\right) \\ 3.P(C\hspace{0.17em}AND\hspace{0.17em}L)=P\left(C\right)P\left(L\right) \end{gathered}$$

Here, if we look at these conditions, first condition $\left(1\right)P\left(C\right|L)=0.55\ne P(C)=0.48$

It is clear that first condition is not satisfied to make both events independent of each other.