Class 12 Probability · Short Answer2 Marksbinomial_distribution
Class 12 Maths · Probability · Short Answer #43
Draw four cards independently with replacement from a 52-card deck. Find P(at least three diamonds).
✅ Step-by-Step Solution
Final Answer: 13/256
- Each draw is a diamond with probability 13/52=1/4. Thus X, the diamond count, has binomial distribution with n=4,p=1/4.
- P(X≥3)=C(4,3)(1/4)³(3/4)+(1/4)⁴=12/256+1/256.
- Therefore P(at least three diamonds)=13/256.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Each draw is a diamond with probability 13/52=1/4. Thus X, the diamond count, has binomial distribution with n=4,p=1/4.
- [1 mark] P(X≥3)=C(4,3)(1/4)³(3/4)+(1/4)⁴=12/256+1/256.
- [0.5 marks] Therefore P(at least three diamonds)=13/256.
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