The marks scored by 100 students are given below:

Marks scored	No. of students
0-10	4
10-20	5
20-30	9
30-40	7
40-50	13
50-60	12
60-70	15
70-80	11
80-90	14
90-100	10

A student in the class is selected at random. Find the probability that the student has scored:

(a) less than 20

(b) below 60 but 30 or more

(c) more than or equal to 70

(d) above 89.

(a) By formula,

Probability that student has scored less than 20

= $\dfrac{\text{No. of students who scored less than 20}}{\text{Total no. of students}} = \dfrac{9}{100}$.

Hence, probability that the student has scored less than 20 = $\dfrac{9}{100}$.

(b) From table,

No. of students who scored less than 60 = 50

No. of students who scored less than 30 = 18

∴ No. of students who score below 60 but 30 or more = 50 - 18 = 32.

Probability that student has scored below 60 but 30 or more = $\dfrac{\text{No. of students scoring between 60 and 30}}{\text{Total no. of students}} = \dfrac{32}{100} = \dfrac{8}{25}$.

Hence, probability that the student has scored below 60 but 30 or more = $\dfrac{8}{25}$.

(c) From table,

No. of students who scored less than 70 = 65

Total no. of students = 100

∴ No. of students who score more than or equal to 70 = 100 - 65 = 35.

Probability that student has scored more than or equal to 70 = $\dfrac{\text{No. of students scoring 70 or more}}{\text{Total no. of students}} = \dfrac{35}{100} = \dfrac{7}{20}$.

Hence, probability that the student has scored more than or equal to 70 = $\dfrac{7}{20}$.

(d) No. of students those who have scored more than 89 = No. of students who has scored between 90-100 = 10.

Probability that student has scored more than 89 = $\dfrac{\text{No. of students scoring \textgreater 89}}{\text{Total no. of students}} = \dfrac{10}{100} = \dfrac{1}{10}$.

Hence, probability that the student has scored more than 89 = $\dfrac{1}{10}$.