A tyre manufacturing company kept a record of the distance covered before a tyre needed to be replaced . The table shows the results of 1000 cases :
`{:("Distance (in km)","less than 4000","4000 to 9000","9001 to 14000","more than 14000"),("Frequency",20,210,325,445):}`
If you buy a tyre of this company , what is the probability that :
it will need to be replaced after it has covered somewhere between 4000 km and 14000 km ?

Answer

To find the probability that a tyre will need to be replaced after it has covered somewhere between 4000 km and 14000 km, we will follow these steps:

### Step 1: Identify the relevant distance ranges
We need to consider the distance ranges that fall between 4000 km and 14000 km. According to the table:
- The distance range from 4000 km to 9000 km has a frequency of 210.
- The distance range from 9001 km to 14000 km has a frequency of 325.

### Step 2: Calculate the total number of favorable cases
To find the total number of favorable cases (tyres that need to be replaced after covering between 4000 km and 14000 km), we add the frequencies of the two relevant ranges:
- Frequency for 4000 to 9000 km = 210
- Frequency for 9001 to 14000 km = 325

Total favorable cases = 210 + 325 = 535

### Step 3: Determine the total number of cases
The total number of cases recorded is given as 1000.

### Step 4: Calculate the probability
The probability \( P \) that a tyre will need to be replaced after covering between 4000 km and 14000 km is calculated using the formula:
\[ P = \frac{\text{Number of favorable cases}}{\text{Total number of cases}} \]
Substituting the values we found:
\[ P = \frac{535}{1000} = 0.535 \]

### Final Answer
The probability that a tyre will need to be replaced after it has covered somewhere between 4000 km and 14000 km is **0.535**.

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