$A$ 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.

  • A
    $\frac{7}{39}, 53/90$
  • B
    $\frac{27}{90}, 69/90$
  • C
    $\frac{7}{19}, 23/90$
  • D
    $\frac{7}{90}, 23/90$

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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.

Fifty 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?

Three 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.

The 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.

Consider 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 $1$.

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