VTU 3rd Sem | BCS301| Maths Module 1 Binomial Distribution Important Question PYQ Easy Explanation

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In this video, we solve one of the most frequently asked and important questions from Module 1 – Probability Distributions of VTU 3rd Sem Mathematics III (BCS301).

🧩 Question Overview:

Question:
The probability of a pen manufactured by a factory being defective is 1/10.
If 12 such pens are manufactured, find the probability that:
1️⃣ Exactly 2 pens are defective
2️⃣ At least 2 pens are defective
3️⃣ None of them are defective

This question is based on the Binomial Probability Distribution, a core concept in VTU’s Mathematics III syllabus under the topic Probability Distributions.

📘 Concepts Explained in This Video:

✅ Understanding Binomial Distribution:
We’ll start by revising the binomial probability formula:
P(X = r) = nCr * pʳ * qⁿ⁻ʳ

Where:

n = number of trials (here, 12 pens)

p = probability of success (defective = 1/10)

q = 1 - p = 9/10

r = number of defective pens

✅ Step-by-Step Calculation:
We’ll calculate the following probabilities with clear explanation and logic:
• P(X = 2) → Exactly 2 defective pens
• P(X ≥ 2) → At least 2 defective pens (using complement method)
• P(X = 0) → None defective

✅ Shortcut Tricks & VTU Tips:
• How to identify when to use binomial vs Poisson distribution
• How to simplify expressions in exams
• Common mistakes to avoid while substituting values

✅ Why This Question Is Important:
This problem tests concept clarity, application of binomial formula, and understanding of “at least / none / exactly” conditions, which are repeatedly asked in VTU exams.

🎯 Learning Outcomes:

After watching this video, you will be able to:
✔ Understand the structure of binomial experiments
✔ Compute probability using the binomial formula confidently
✔ Solve PYQs and expected questions from Module 1
✔ Write step-by-step solutions for VTU exams
✔ Gain clarity on exam-focused concepts of Probability Distribution

🧾 Topics Covered in This Video:

• Binomial Distribution Formula and Concept
• Probability of Defective Items
• Complementary Probability Method (P(X ≥ 2))
• Real-life interpretation of the problem
• Expected value and VTU pattern analysis

🎓 Perfect For:
• VTU 3rd Sem Students (CSE / ISE / AIML / DS)
• 2022 & 2023 Scheme (Mathematics III – BCS301)
• Students preparing for VTU 2025 Exams
• Learners studying Probability and Statistics



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VTU 3rd Sem Maths Module 1
Binomial Distribution Problem
Important Question + Easy Explanation