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 mutually exclusive events? Show why or why not.

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.

Now solving,

$$\begin{gathered} P\left(L\right)=0.376 \\ P\left(C\right)=0.48 \\ P(C\mid L)=0.55 \\ \frac{P(C\cap L)}{0.376}=0.55 \\ P(C\cap L)=0.55\times 0.376 \\ P(C\cap L)=0.2068 \end{gathered}$$

L and C Denotes a person who is Latino Californian registered voter who prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Here, $55\%$of people among Latino Californians who prefer life in prison without parole over the death penalty for a person convicted of first degree murder and there are $37.6\%$people who are Latino Californians among whole Californians.

No, L and C are not mutually exclusive because$P(C\cap L)\ne 0.$