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 last more than 9000 km ?

Answer

To find the probability that a tyre will last more than 9000 km, we can follow these steps:

### Step 1: Identify the total number of cases
The total number of cases given in the problem is 1000.

### Step 2: Determine the frequency of tyres lasting more than 9000 km
From the table, the distances and their corresponding frequencies are:
- Less than 4000 km: 20
- 4000 to 9000 km: 210
- 9001 to 14000 km: 325
- More than 14000 km: 445

To find the total number of tyres that last more than 9000 km, we need to add the frequencies of the last two categories:
- Frequency of tyres lasting 9001 to 14000 km: 325
- Frequency of tyres lasting more than 14000 km: 445

Calculating this gives:
\[ 325 + 445 = 770 \]

### Step 3: Calculate the probability
The probability \( P \) that a tyre lasts more than 9000 km is given by the formula:
\[ P(\text{more than 9000 km}) = \frac{\text{Number of favourable cases}}{\text{Total number of cases}} \]

Substituting the values we found:
\[ P(\text{more than 9000 km}) = \frac{770}{1000} \]

### Step 4: Simplify the probability
Now, we can simplify this fraction:
\[ P(\text{more than 9000 km}) = 0.77 \]

### Final Answer
The probability that a tyre will last more than 9000 km is \( 0.77 \).

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