The manager of a used car took inventory of the automobiles on his lot and constructed the following table based on the age of his car in years and it's make ( foreign or domestic). A car was randomly selected from the lot. What is the probability that a car was older than 2 years given that the car selected was a foreign car?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The manager of a used car took inventory of the automobiles on his lot and constructed the following table based on the age of his car in years and it's make ( foreign or domestic). A car was randomly selected from the lot. What is the
![### Probability in Automobile Inventory
#### Problem Statement
The manager of a used car lot took an inventory of the automobiles based on their age and make (foreign or domestic). A car was randomly selected. What is the probability that the car selected was a foreign car?
#### Table Data
The table below shows the number of cars based on their make and age group:
| Make | 0 - 2 years | 3 - 5 years | 6 - 10 years | Over 10 years | Total |
|---------|-------------|-------------|--------------|---------------|-------|
| Foreign | 36 | 28 | 14 | 22 | 100 |
| Domestic| 44 | 27 | 12 | 17 | 100 |
| Total | 80 | 55 | 26 | 39 | 200 |
#### Explanation
- **Foreign Cars:**
- 0 - 2 years: 36
- 3 - 5 years: 28
- 6 - 10 years: 14
- Over 10 years: 22
- **Total Foreign Cars:** 100
- **Domestic Cars:**
- 0 - 2 years: 44
- 3 - 5 years: 27
- 6 - 10 years: 12
- Over 10 years: 17
- **Total Domestic Cars:** 100
- **Overall Total Cars:** 200
#### Objective
Determine the probability a randomly selected car is foreign.
#### Solution
The probability of selecting a foreign car is given by dividing the total number of foreign cars by the total number of cars.
\[ P(\text{Foreign}) = \frac{\text{Total Foreign Cars}}{\text{Total Cars}} = \frac{100}{200} = \frac{1}{2} \]
The probability that a randomly selected car is foreign is \( \frac{1}{2} \) or 50%.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb27aec09-4413-42f4-8ddd-e0b51dd64302%2F4f08f2f2-99d1-4d15-85d2-4ffa70523cbf%2F2hffe5u_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
