Question

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:

1. less than 20. 
2. below 60 but 30 or more. 
3. more than or equal to 70. 
4. above 89.

Answer 1

Given: Marks distribution for 100 students is 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.

Step-wise calculation: 

a. Probability (score < 20):

Counts for < 20

= 0 – 10 + 10 – 20 

= 4 + 5

= 9

`P = 9/100`

= 0.09

b. Probability (30 ≤ score < 60) below 60 but 30 or more:

Counts = 30 – 40 + 40 – 50 + 50 – 60

= 7 + 13 + 12

= 32

`P = 32/100`

= 0.32

c. Probability (score ≥ 70):

Counts = 70 – 80 + 80 – 90 + 90 – 100

= 11 + 14 + 10

= 35

`P = 35/100`

= 0.35

d. Probability (score > 89):

Scores > 89 fall into 90 – 100 class = 10

`P = 10/100`

= 0.10