Thank you for the correction. If the number of students who scored full marks in Section C is 4 instead of 5, we need to adjust the calculations accordingly.

Updated Information:

• Number of students who scored full marks from each section:
  • Section A: 2 students
  • Section B: 3 students
  • Section C: 4 students (corrected)
  • Section D: 5 students

Updated Calculations:

Question 1:

What is the probability that a student picked randomly from the MBA batch scored full marks in the quiz?

1. Total number of students across all sections remains the same: $\text{Total students} = 240 \text{ students}$

2. Total number of students who scored full marks: $\text{Total full marks} = 2 + 3 + 4 + 5 = 14 \text{ students}$

3. Probability that a randomly selected student scored full marks: $P(\text{Full marks}) = \frac{14}{240} = \frac{7}{120}$

Question 2:

If a student who scored full marks is selected, what is the probability that he/she is from Section A?

1. Conditional Probability (using the corrected data): $P(\text{Section A | Full marks}) = \frac{\frac{2}{240}}{\frac{14}{240}} = \frac{2}{14} = \frac{1}{7}$

Final Updated Answers:

1. Probability that a randomly selected student scored full marks: $\frac{7}{120}$.
2. Probability that a student is from Section A given that they scored full marks: $\frac{1}{7}$.

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Let me know if you need further explanation or have additional questions!

Follow-up Questions:

1. How does the reduction in Section C's full marks students affect the overall probability of selecting a full marks student?
2. What is the probability that a student from Section D scored full marks?
3. How would these probabilities change if the number of students in the batch increased?
4. Can you calculate the expected number of full marks students in any randomly selected group of 10 students?
5. How can the concept of joint probability be applied to this scenario?

Tip:

When handling conditional probabilities, ensure that all relevant information is accurately reflected in your calculations. Small changes in the data can significantly affect the results.