Class 12 Probability · Long Answer3 Marksbinomial_distribution
Class 12 Maths · Probability · Long Answer #108
A box has20 pens,2 defective. Draw5 independently with replacement. Find P(at most2 defective).
✅ Step-by-Step Solution
Final Answer: 12393/12500=0.99144
- The defective probability is 2/20=1/10 on every independent draw. Let X~Binomial(5,1/10).
- P(X≤2)=Σₖ₌₀²C(5,k)(1/10)ᵏ(9/10)^(5−k).
- The numerator over 10⁵ is 9⁵+5·9⁴+10·9³=59049+32805+7290=99144.
- Thus P(X≤2)=99144/100000=12393/12500=0.99144.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The defective probability is 2/20=1/10 on every independent draw. Let X~Binomial(5,1/10).
- [1 mark] P(X≤2)=Σₖ₌₀²C(5,k)(1/10)ᵏ(9/10)^(5−k).
- [1 mark] The numerator over 10⁵ is 9⁵+5·9⁴+10·9³=59049+32805+7290=99144.
- [0.5 marks] Thus P(X≤2)=99144/100000=12393/12500=0.99144.
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