Question
The table given below shows the marks obtained by $30$ students in a test.
Marks
$($Class interval$)$
$1 - 10$ $11 - 20$ $21 - 30$ $31 - 40$ $41 - 50$
Number of students
$($Frequency$)$
$7$ $10$ $6$ $4$ $3$
Out of these students, one is chosen at random. What is the probability that the marks of the chosen student:
$i.$ Are $30$ or less?
$ii.$ Are $31$ or more?
$iii.$ Lie in the interval $21 - 30$?

Answer

Total number of students $= 30$
$i.$ Probability that the marks of the chosen student are $30$ or less $=\frac{7+10+6}{30}=\frac{23}{30}$
$ii.$ Probability that the marks of the chosen student are $31$ or less $=\frac{4+3}{30}=\frac{7}{30}$
$iii.$ Probability that the marks of the chosen student lie in the interval $21 - 30 =\frac{6}{30}=\frac{1}{5}$

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