The problem is to find the probability of a student scoring certain marks based on a given table showing the marks scored by 40 students. a) Find the probability that a student scored marks greater than 28. b) Find the probability that a student scored marks less than 28. c) Find the probability that a student scored 33 marks. d) Find the probability that a student scored marks between 3 and 33.

1. Problem Description

The problem is to find the probability of a student scoring certain marks based on a given table showing the marks scored by 40 students.

a) Find the probability that a student scored marks greater than

2

8. b) Find the probability that a student scored marks less than

2

8. c) Find the probability that a student scored 33 marks.

d) Find the probability that a student scored marks between 3 and

3

3.

2. Solution Steps

First, we need to find the total number of students. From the image, the total number of students is calculated as:

$2 + 5 + 9 + 6 + 3 + 4 + 5 + 1 = 35$

So, the total number of students is

3

5.

a) Marks greater than 28:

The marks greater than 28 are 33 and

3

8. The number of students who scored 33 is

5. The number of students who scored 38 is

1. The total number of students who scored greater than 28 is $5 + 1 = 6$.

The probability of a student scoring greater than 28 is $\frac{6}{35}$.

b) Marks less than 28:

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

2

3. The number of students who scored 3 is

2. The number of students who scored 8 is

5. The number of students who scored 13 is

9. The number of students who scored 18 is

6. The number of students who scored 23 is

3. The total number of students who scored less than 28 is $2 + 5 + 9 + 6 + 3 = 25$.

The probability of a student scoring less than 28 is $\frac{25}{35} = \frac{5}{7}$.

c) 33 marks:

The number of students who scored 33 marks is

5. The probability of a student scoring 33 marks is $\frac{5}{35} = \frac{1}{7}$.

d) Between 3 and 33 marks:

This means the marks are greater than or equal to 3 and less than or equal to

3

3. So the marks are 3, 8, 13, 18, 23, 28, and

3

3. The number of students who scored 3 is

2. The number of students who scored 8 is

5. The number of students who scored 13 is

9. The number of students who scored 18 is

6. The number of students who scored 23 is

3. The number of students who scored 28 is

4. The number of students who scored 33 is

5. The total number of students who scored between 3 and 33 marks is $2 + 5 + 9 + 6 + 3 + 4 + 5 = 34$.

The probability of a student scoring between 3 and 33 marks is $\frac{34}{35}$.

3. Final Answer

a) $\frac{6}{35}$

b) $\frac{5}{7}$

c) $\frac{1}{7}$

d) $\frac{34}{35}$