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.

Find P(L OR C) to four decimal places.

To solve for \( P(L \text{ OR } C) \), we can use the **Addition Rule** for probabilities. This rule is given by:

\[
P(A \text{ OR } B) = P(A) + P(B) - P(A \text{ AND } B)
\]

In this context:
- \( P(L) \) is the probability that a randomly selected Californian is Latino.
- \( P(C) \) is the probability that a randomly selected Californian prefers life in prison without parole over the death penalty.
- \( P(L \text{ AND } C) \) is the probability that a randomly selected Californian is both Latino and prefers life in prison without parole.

Let's break it down:

### Given information:
- \( P(C) = 0.48 \) (48% of all Californians prefer life in prison without parole).
- \( P(L) = 0.376 \) (37.6% of all Californians are Latino).
- \( P(C \mid L) = 0.55 \) (55% of Latinos prefer life in prison without parole).

### Step 1: Find \( P(L \text{ AND } C) \)
We need to find \( P(L \text{ AND } C) \), which represents the probability that a randomly selected Californian is both Latino and prefers life in prison without parole. This is calculated as:

\[
P(L \text{ AND } C) = P(L) \times P(C \mid L)
\]

Substitute the given values:

\[
P(L \text{ AND } C) = 0.376 \times 0.55 = 0.2068
\]

### Step 2: Apply the Addition Rule
Now we can apply the addition rule to find \( P(L \text{ OR } C) \):

\[
P(L \text{ OR } C) = P(L) + P(C) - P(L \text{ AND } C)
\]

Substitute the known values:

\[
P(L \text{ OR } C) = 0.376 + 0.48 - 0.2068 = 0.6492
\]

Thus, the probability that a randomly selected Californian is either Latino or prefers life in prison without parole over the death penalty is:

\[
P(L \text{ OR } C) = 0.6492
\]

### Final Answer:
\[
P(L \text{ OR } C) = 0.6492
\]

Let me know if you'd like more details on this or have any further questions!

Here are 5 related questions:
1. How would the probability change if 60% of Latinos preferred life in prison without parole?
2. What is the probability that a randomly selected Californian is neither Latino nor prefers life in prison without parole?
3. How would the result be affected if 50% of all Californians preferred life in prison without parole?
4. What is \( P(C \mid L^c) \), the probability that a non-Latino prefers life in prison without parole?
5. How would you compute the probability if given data for another demographic group, such as African Americans?

**Tip**: The "Addition Rule" is very useful when calculating the probability of either event occurring, but be mindful to subtract the overlap between events!

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. Suppose that one Californian is randomly selected. Find P(L OR C) to four decimal places.

Find the probability that a randomly selected Californian is either Latino or prefers life in prison without parole over the death penalty. This problem explores key probability concepts, including the addition rule and conditional probability, with data on California registered voters and Latinos.

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