Binomial Distribution - Example Problem 2 | Probability Distribution | Engineering Mathematics

📘 Binomial Probability Problems – Important Solved Examples In this video, we solve step-by-step exam-focused problems using the Binomial Distribution. These questions are frequently asked in university exams and competitive tests, so watch carefully for the standard shortcuts and reasoning. 🔢 Questions Covered in this Video: Question 1 (00:20) A consignment of electrical lamps contains 5% defective lamps. If a random sample of 8 lamps is inspected, find the probability that one or more are defective. (Use the complement rule: P(one or more defective) = 1 − P(none defective).) Question 2 (04:31) The probability that a person aged 60 lives up to 70 years is 0.65. What is the probability that out of 10 such persons, at least 7 of them live up to 70? (Compute P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) using the binomial formula.) ✨ What You’ll Learn in This Video: ✔ How to apply the Binomial probability formula: nCk · p^k · (1−p)^(n−k) ✔ When and how to use the complement rule to simplify calculations ✔ How to compute “one or more” and “at least” probabilities efficiently ✔ Exam-focused tips and quick shortcuts for computing cumulative binomial probabilities ✔ Useful for VTU, B.Sc., B.E., B.Tech., and competitive exams 📌 Make sure to watch till the end for full solutions and quick tricks! 📘 Probability Distributions – VTU BCS301 Module 1 🎥 Full Playlist (Autoplay all problems) https://www.youtube.com/playlist?list=PLM9RnGtTy9_-Xd_PmY1uXnHZ1LrXCB8N- 📌 Problems with Direct Links: 1️⃣ Coin & Die Problems – https://youtu.be/_8Zk8FuhDsE 2️⃣ Discrete Distribution (Mean & Var) – https://youtu.be/QqI7nJLrP0I 3️⃣ Find k, Mean & Std Dev – https://youtu.be/Kgd8qjBf-f8 4️⃣ Perished Apples Distribution – https://youtu.be/NBqEhyVK-T4 5️⃣ Probability Function (Find k & P(x)) – https://youtu.be/fPvW4izc0aM 6️⃣ Distribution P(x)=kx (Mean & Var) – https://youtu.be/JV0M3Sf4yRU 7️⃣ Binomial (Mean & Std Dev) – https://youtu.be/B_LgSxsYHZU 8️⃣ Binomial (Coin Toss & Def Pens) – https://youtu.be/UCJ7wN52lrw 9️⃣ Binomial (Def Lamps & Survival) – https://youtu.be/S62yQdSNAZ0 🔟 Binomial (Telephone & Quiz) – https://youtu.be/UX45WcMTyB4 1️⃣1️⃣ Poisson (Defectives in Samples) – https://youtu.be/iW4oBFDzAZ8 1️⃣2️⃣ Poisson (Students Test) – https://youtu.be/5LZGgkD5oF4 1️⃣3️⃣ Airline Seats & Families – https://youtu.be/8jb1RL-XnE0 1️⃣4️⃣ Fitting Binomial (Dice & Coins) – https://youtu.be/hfijBm3gREE 1️⃣5️⃣ Poisson (Mean & SD) – https://youtu.be/d7-z9y8CKp8 1️⃣6️⃣ Fit Poisson (Accidents Data) – https://youtu.be/fr84-j_c4f4 1️⃣7️⃣ Poisson (Blades & Fuses) – https://youtu.be/MjiEem7DmqY 1️⃣8️⃣ Poisson (Injection Reactions) – https://youtu.be/MZA0Str3wIE 1️⃣9️⃣ PDF f(x)=(x/6)+c – https://youtu.be/DwenlGtlEbw 2️⃣0️⃣ PDF f(x)=kx² (0 to 3)– https://youtu.be/H-xgw8JJkoc 2️⃣1️⃣ PDF f(x)=kx² [-3 to 3] – https://youtu.be/Ui91zRVvlaA 2️⃣2️⃣ PDF f(x)=kx·e^(-x) – https://youtu.be/9wRCZv4E1l8 2️⃣3️⃣ Exponential (Mean=3) – https://youtu.be/ZIJDFUmUW6k 2️⃣4️⃣ Exponential (Mean=5) – https://youtu.be/whINMS95qvk 2️⃣5️⃣ Exponential (Calls) – https://youtu.be/PZx5FZ_8N3M 2️⃣6️⃣ Exponential (Showers) – https://youtu.be/LXlkyEIfKGA 2️⃣7️⃣ Normal (Mean=30, SD=5) – https://youtu.be/tawEPP76zZg 2️⃣8️⃣ Normal (1000 Students Marks) – https://youtu.be/thmpqNzHy98 2️⃣9️⃣ Normal (Bulb Lifetime) – https://youtu.be/1VqRlWwn4QE 3️⃣0️⃣ Normal (Find Mean & SD) – https://youtu.be/xfXAB36pVGM 3️⃣1️⃣ Normal (Exam Marks) – https://youtu.be/7HOQD4roabU 💡 Support our work: 👉 https://www.youtube.com/channel/UC_OTtwh8_-q-bA7DoS--syg/join #BinomialDistribution #ProbabilityDistribution #StatisticsProblems #ExamPreparation #EngineeringMathematics #VTUExam #BScMaths #BTechMaths #Probability #MathsSolutions #StepByStepMaths