Question

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)	Frequency
Less than 4000	20
4000 to 9000	210
9001 to 14000	325
More than 14000	445

If you buy a tyre from this company, what is the probability that it will need to be replaced after it has covered a distance somewhere between 4000 km and 14000 km?
(a) 0.65
(a) 0.625
(a) 0.125
(a) None of these

Answer 1

Hint: Find the number of cases when the tire is replaced between 4000 km and 14000 km by adding the number of cases between 4000 km and 9000 km and the number of cases between 9000 km and 14000 km. Divide this number by the total number of cases (1000) to get the final answer.

Complete step-by-step solution
In this question, we are given that 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)	Frequency
Less than 4000	20
4000 to 9000	210
9001 to 14000	325
More than 14000	445

If we buy a tyre from this company, we need to find the probability that it will need to be replaced after it has covered a distance somewhere between 4000 km and 14000 km.
Let A be the event that the tyre needs to be replaced after it has covered a distance somewhere between 4000 km and 14000 km.
Number of the case when the tire is replaced between 4000 km and 14000 km = Number of cases between 4000 km and 9000 km + Number of cases between 9000 km and 14000 km
Number of case when tyre is replaced between 4000 km and 14000 km = 210 + 325 = 535
So, the number of favorable cases = 535
Also, the total number of cases = 1000
So, the probability that the tyre needs to be replaced after it has covered a distance somewhere between 4000 km and 14000 km is given by:
$P\left( A \right)=\dfrac{535}{1000}=0.535$
Hence, option (d) is correct.

Note: In this question, it is very important to know the concept and the formula for probability. The probability for an event A to happen is given by the following:
$P\left( A \right)=\dfrac{\text{No}\text{. of favourable outcomes}}{\text{Total no}\text{. of outcomes}}$