The problem asks to find the probability of certain events based on the marks scored by 40 students in an objective test. The distribution of marks is given in a table. We need to find the probabilities for: a) Marks greater than 28 b) Marks less than 28 c) 33 marks d) Marks between 3 and 33 (inclusive).

1. Problem Description

The problem asks to find the probability of certain events based on the marks scored by 40 students in an objective test. The distribution of marks is given in a table. We need to find the probabilities for:

a) Marks greater than 28

b) Marks less than 28

c) 33 marks

d) Marks between 3 and 33 (inclusive).

2. Solution Steps

First, we need to find the total number of students, which is given as

4

0.

a) Marks greater than 28:

The marks greater than 28 are 33 and

3

8. Number of students with 33 marks = 5

Number of students with 38 marks = 1

Total number of students with marks greater than 28 = 5 + 1 = 6

Probability = $\frac{\text{Number of students with marks > 28}}{\text{Total number of students}} = \frac{6}{40} = \frac{3}{20}$

b) Marks less than 28:

The marks less than 28 are 3, 8, 13, 18, and

2

3. Number of students with 3 marks = 2

Number of students with 8 marks = 5

Number of students with 13 marks = 9

Number of students with 18 marks = 6

Number of students with 23 marks = 3

Total number of students with marks less than 28 = 2 + 5 + 9 + 6 + 3 = 25

Probability = $\frac{\text{Number of students with marks < 28}}{\text{Total number of students}} = \frac{25}{40} = \frac{5}{8}$

c) 33 marks:

Number of students with 33 marks = 5

Probability = $\frac{\text{Number of students with 33 marks}}{\text{Total number of students}} = \frac{5}{40} = \frac{1}{8}$

d) Between 3 and 33 marks (inclusive):

Marks include 3, 8, 13, 18, 23, 28, 33

Number of students with 3 marks = 2

Number of students with 8 marks = 5

Number of students with 13 marks = 9

Number of students with 18 marks = 6

Number of students with 23 marks = 3

Number of students with 28 marks = 4

Number of students with 33 marks = 5

Total number of students with marks between 3 and 33 = 2 + 5 + 9 + 6 + 3 + 4 + 5 = 34

Probability = $\frac{\text{Number of students with marks between 3 and 33}}{\text{Total number of students}} = \frac{34}{40} = \frac{17}{20}$

3. Final Answer

a) The probability of marks greater than 28 is $\frac{3}{20}$.

b) The probability of marks less than 28 is $\frac{5}{8}$.

c) The probability of 33 marks is $\frac{1}{8}$.

d) The probability of marks between 3 and 33 (inclusive) is $\frac{17}{20}$.