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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.

Short Answer

Expert verified

No, L and C are not mutually exclusive because P(CL)0.

Step by step solution

01

Given information

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.
02

Calculation

Now solving,

P(L)=0.376P(C)=0.48P(CL)=0.55P(CL)0.376=0.55P(CL)=0.550.376P(CL)=0.2068

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.

03

Final answer

No, L and C are not mutually exclusive becauseP(CL)0.

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