$A$ teacher wanted to analyze the performance of two sections of students in a mathematics test of $100$ marks. Looking at their performances,she found that a few students got under $20$ marks and a few got $70$ marks or above. So she decided to group them into intervals of varying sizes as follows: $0-20, 20-30, ..., 60-70, 70-100$. Then she formed the following table:
Marks Number of students $0-20$ $7$ $20-30$ $10$ $30-40$ $10$ $40-50$ $20$ $50-60$ $20$ $60-70$ $15$ $70$ and above $8$ Total $90$
$(i)$ Find the probability that a student obtained less than $20\%$ in the mathematics test.
$(ii)$ Find the probability that a student obtained marks $60$ or above.
| Marks | Number of students |
| $0-20$ | $7$ |
| $20-30$ | $10$ |
| $30-40$ | $10$ |
| $40-50$ | $20$ |
| $50-60$ | $20$ |
| $60-70$ | $15$ |
| $70$ and above | $8$ |
| Total | $90$ |
$(i)$ Find the probability that a student obtained less than $20\%$ in the mathematics test.
$(ii)$ Find the probability that a student obtained marks $60$ or above.
- A$\frac{7}{39}, 53/90$
- B$\frac{27}{90}, 69/90$
- C$\frac{7}{19}, 23/90$
- D$\frac{7}{90}, 23/90$
Explore More
Similar Questions
$A$ die is thrown $1000$ times with the frequencies for the outcomes $1, 2, 3, 4, 5$ and $6$ as given in the following table:
Outcome $1$ $2$ $3$ $4$ $5$ $6$ Frequency $179$ $150$ $157$ $149$ $175$ $190$
Find the probability of getting each outcome.
| Outcome | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ |
| Frequency | $179$ | $150$ | $157$ | $149$ | $175$ | $190$ |
Find the probability of getting each outcome.
Medium
View SolutionFifty seeds were selected at random from each of $5$ bags of seeds,and were kept under standardised conditions favourable to germination. After $20$ days,the number of seeds which had germinated in each collection were counted and recorded as follows:
Bag $1$ $2$ $3$ $4$ $5$ Number of seeds germinated $40$ $48$ $42$ $39$ $41$
What is the probability of germination of
$(i)$ more than $40$ seeds in a bag?
$(ii)$ $49$ seeds in a bag?
$(iii)$ more than $35$ seeds in a bag?
| Bag | $1$ | $2$ | $3$ | $4$ | $5$ |
| Number of seeds germinated | $40$ | $48$ | $42$ | $39$ | $41$ |
What is the probability of germination of
$(i)$ more than $40$ seeds in a bag?
$(ii)$ $49$ seeds in a bag?
$(iii)$ more than $35$ seeds in a bag?
Medium
View SolutionThree coins are tossed simultaneously $200$ times with the following frequencies of different outcomes:
Outcome $3$ heads $2$ heads $1$ head No head Frequency $23$ $72$ $77$ $28$
If the three coins are simultaneously tossed again,compute the probability of $2$ heads coming up.
| Outcome | $3$ heads | $2$ heads | $1$ head | No head |
| Frequency | $23$ | $72$ | $77$ | $28$ |
If the three coins are simultaneously tossed again,compute the probability of $2$ heads coming up.
Medium
View SolutionThe percentage of marks obtained by a student in the monthly unit tests are given below:
Unit test $I$ $II$ $III$ $IV$ $V$ Percentage of marks obtained $69$ $71$ $73$ $68$ $74$
Based on this data,find the probability that the student gets more than $70\%$ marks in a unit test.
| Unit test | $I$ | $II$ | $III$ | $IV$ | $V$ |
| Percentage of marks obtained | $69$ | $71$ | $73$ | $68$ | $74$ |
Based on this data,find the probability that the student gets more than $70\%$ marks in a unit test.
Medium
View SolutionConsider the frequency distribution table which gives the weights of $38$ students of a class.
Weights (in $kg$) Number of students $31-35$ $9$ $36-40$ $5$ $41-45$ $14$ $46-50$ $3$ $51-55$ $1$ $56-60$ $2$ $61-65$ $2$ $66-70$ $1$ $71-75$ $1$ Total $38$
$(i)$ Find the probability that the weight of a student in the class lies in the interval $46-50 \, kg$.
$(ii)$ Give two events in this context,one having probability $0$ and the other having probability $1$.
| Weights (in $kg$) | Number of students |
| $31-35$ | $9$ |
| $36-40$ | $5$ |
| $41-45$ | $14$ |
| $46-50$ | $3$ |
| $51-55$ | $1$ |
| $56-60$ | $2$ |
| $61-65$ | $2$ |
| $66-70$ | $1$ |
| $71-75$ | $1$ |
| Total | $38$ |
$(i)$ Find the probability that the weight of a student in the class lies in the interval $46-50 \, kg$.
$(ii)$ Give two events in this context,one having probability $0$ and the other having probability $1$.
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo