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ICSE Class 10 Mathematics Question 8 of 28

Short Answer Questions 2 — Question 8

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Question 85

The marks scored by 100 students are given below:

Marks scoredNo. of students
0-104
10-205
20-309
30-407
40-5013
50-6012
60-7015
70-8011
80-9014
90-10010

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.

Answer
Marks scoredNo. of studentsCumulative frequency
0-1044
10-2059
20-30918
30-40725
40-501338
50-601250
60-701565
70-801176
80-901490
90-10010100

(a) By formula,

Probability that student has scored less than 20

= No. of students who scored less than 20Total no. of students=9100\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 = 9100\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 = No. of students scoring between 60 and 30Total no. of students=32100=825\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 = 825\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 = No. of students scoring 70 or moreTotal no. of students=35100=720\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 = 720\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 = No. of students scoring >89Total no. of students=10100=110\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 = 110\dfrac{1}{10}.