The image contains a frequency distribution table in Gujarati along with two questions:

Frequency Table:

• મેળવેલ ગુણ (Marks Obtained): 20, 25, 28, 29, 33, 38, 42, 43
• વિદ્યાર્થીની સંખ્યા (Number of Students): 6, 20, 24, 28, 15, 4, 2, 1

Questions:

1. Find the probability of students scoring more than 40 marks.
2. Find the probability of students scoring less than 30 marks.

Solution:

1. Probability of students scoring more than 40 marks:

   Marks greater than 40 are: 42 and 43.

   • Number of students scoring 42 marks = 2
   • Number of students scoring 43 marks = 1

   So, the total number of students scoring more than 40 marks is $2 + 1 = 3$.

   The total number of students is: $6 + 20 + 24 + 28 + 15 + 4 + 2 + 1 = 100$

   Therefore, the probability $P$ of students scoring more than 40 marks is: $P(\text{marks} > 40) = \frac{3}{100} = 0.03$

2. Probability of students scoring less than 30 marks:

   Marks less than 30 are: 20, 25, and 28.

   • Number of students scoring 20 marks = 6
   • Number of students scoring 25 marks = 20
   • Number of students scoring 28 marks = 24

   So, the total number of students scoring less than 30 marks is $6 + 20 + 24 = 50$.

   Therefore, the probability $P$ of students scoring less than 30 marks is: $P(\text{marks} < 30) = \frac{50}{100} = 0.50$

Would you like more detailed explanations or have any further questions?

Related Questions:

1. What is the probability of students scoring exactly 33 marks?
2. How do we calculate cumulative probabilities in such distributions?
3. Can we calculate the mean score from the given data?
4. How would you calculate the median score from the data provided?
5. What is the probability of students scoring between 30 and 40 marks?

Tip:

When calculating probabilities from a frequency distribution, always ensure the total number of observations (students, in this case) is correctly summed for accuracy.