$A$ 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:
$(i)$ it will need to be replaced before it has covered $4000 \, km$?
$(ii)$ it will last more than $9000 \, km$?
$(iii)$ it will need to be replaced after it has covered somewhere between $4000 \, km$ and $14000 \, km$?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) $(i)$ The total number of trials $= 1000$.
The frequency of a tyre that needs to be replaced before it covers $4000 \, km$ is $20$.
So,$P(\text{tyre to be replaced before it covers } 4000 \, km) = \frac{20}{1000} = 0.02$.
$(ii)$ The frequency of a tyre that will last more than $9000 \, km$ is the sum of frequencies for the ranges $9001$ to $14000$ and more than $14000$,which is $325 + 445 = 770$.
So,$P(\text{tyre will last more than } 9000 \, km) = \frac{770}{1000} = 0.77$.
$(iii)$ The frequency of a tyre that requires replacement between $4000 \, km$ and $14000 \, km$ is the sum of frequencies for the ranges $4000$ to $9000$ and $9001$ to $14000$,which is $210 + 325 = 535$.
So,$P(\text{tyre requiring replacement between } 4000 \, km \text{ and } 14000 \, km) = \frac{535}{1000} = 0.535$.

Explore More

Similar Questions

An insurance company selected $2000$ drivers at random in a particular city to find a relationship between age and accidents. The data obtained are given in the following table:
Age of drivers (in years) $0$ accidents $1$ accident $2$ accidents $3$ accidents Over $3$ accidents
$18-29$ $440$ $160$ $110$ $61$ $35$
$30-50$ $505$ $125$ $60$ $22$ $18$
Above $50$ $360$ $45$ $35$ $15$ $9$

Find the probabilities of the following events for a driver chosen at random from the city:
$(i)$ Being $18-29$ years of age and having exactly $3$ accidents in one year.
$(ii)$ Being $30-50$ years of age and having one or more accidents in a year.
$(iii)$ Having no accidents in one year.

To know the opinion of the students about the subject statistics,a survey of $200$ students was conducted. The data is recorded in the following table.
Opinion Number of students
Like $135$
Dislike $65$

Find the probability that a student chosen at random:
$(i)$ likes statistics,$(ii)$ does not like it.

On one page of a telephone directory,there were $200$ telephone numbers. The frequency distribution of their unit place digit (for example,in the number $25828573$,the unit place digit is $3$) is given in the table below:
Digit $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$
Frequency $22, 26, 22, 22, 20, 10, 14, 28, 16, 20$

Without looking at the page,a number is chosen at random. What is the probability that the digit in its unit place is $6$?

$1500$ families with $2$ children were selected randomly,and the following data were recorded:
Number of girls in a family $2$ $1$ $0$
Number of families $475$ $814$ $211$

Compute the probability of a family,chosen at random,having:
$(i)$ $2$ girls $(ii)$ $1$ girl $(iii)$ No girl
Also,check whether the sum of these probabilities is $1$.

Difficult
View Solution

Ask all the students in your class to write a $3-$digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by $3$? Remember that a number is divisible by $3$,if the sum of its digits is divisible by $3$.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo