The following frequency distribution shows the number of cars owned by the 20 families on Pearl Street .
`{:(x,"The number of families having x number of cars"),(1,2),(2,2),(3,a),(4,4),(5,5),(6,2):}`
What is the probability that a family randomly selected from the street has at least 4 cars?

Options

A. `1//10`
B. `1//5`
C. `3//10`
D. `11//20`

Answer

To solve the problem of finding the probability that a randomly selected family from Pearl Street has at least 4 cars, we can follow these steps:

### Step 1: Understand the Frequency Distribution
The frequency distribution provided is:
- 1 car: 2 families
- 2 cars: 2 families
- 3 cars: a families (we will assume a = 2 for this example)
- 4 cars: 4 families
- 5 cars: 5 families
- 6 cars: 2 families

### Step 2: Identify Families with at Least 4 Cars
"At least 4 cars" means we need to consider families that have 4, 5, or 6 cars. We will sum the number of families for these categories:
- Families with 4 cars: 4
- Families with 5 cars: 5
- Families with 6 cars: 2

Total families with at least 4 cars = 4 + 5 + 2 = 11 families.

### Step 3: Calculate Total Number of Families
The total number of families surveyed is given as 20.

### Step 4: Calculate the Probability
The probability \( P \) of selecting a family that has at least 4 cars is given by the formula:
\[ P(\text{at least 4 cars}) = \frac{\text{Number of families with at least 4 cars}}{\text{Total number of families}} \]
Substituting the values we found:
\[ P(\text{at least 4 cars}) = \frac{11}{20} \]

### Step 5: Conclusion
The probability that a randomly selected family has at least 4 cars is \( \frac{11}{20} \).