3) What is the probability that a resident owns a house but not a car? Check Show answer
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Hi. I need assistance with question #3. I am not sure how to divide 46 with the information provided.
![**Activity: Applying the Addition Rule and Complements**
In a certain city, 46% of residents own a house, 67% of residents own a car, and 21% of residents own both a house and a car.
Let \( A \) be the event that a randomly selected resident from the city owns a house and \( B \) be the event that a randomly selected resident from the city owns a car.
1) **What is the probability that a resident owns a house, a car, or both?**
Input: 0.92
- **Check**
- **Show answer**
**Correct Answer:**
- The addition rule is used to find \( P(A \cup B) \):
\[
P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.46 + 0.67 - 0.21 = 0.92
\]
2) **What is the probability that a resident owns neither a house nor a car?**
Input: 0.08
- **Check**
- **Show answer**
**Correct Answer:**
- The event that a resident owns neither a house nor a car is \( \overline{A \cup B} \).
- The complement rule is used to find \( P(\overline{A \cup B}) \):
\[
P(\overline{A \cup B}) = 1 - P(A \cup B)
= 1 - 0.92
= 0.08
\]
3) **What is the probability that a resident owns a house but not a car?**
Input: Not provided
- **Check**
- **Show answer**
**Incorrect Answer Explanation:**
- The event \( A \) can be divided into two mutually exclusive events: the event that a resident owns a house and a car, and the event that a resident owns a house but not a car.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed1e02d0-7fec-4353-b680-bbaf407d05ef%2F3f0df87f-2a68-43e6-a27c-eb12941c1a15%2Ftmprmq_processed.jpeg&w=3840&q=75)
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