Class 12 Probability · Long Answer3 Marksindependence
Class 12 Maths · Probability · Long Answer #107
A,B independently fire once at a target with hit probabilities 1/3,2/5. Find (i) P(target hit); (ii) P(exactly one hit).
✅ Step-by-Step Solution
Final Answer: (i) 3/5; (ii) 7/15
- Independent misses have probability (2/3)(3/5)=2/5.
- Thus P(at least one hit)=1−2/5=3/5.
- Exactly one hit has probability (1/3)(3/5)+(2/3)(2/5)=1/5+4/15=7/15.
- The answers are 3/5 and 7/15, respectively.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Independent misses have probability (2/3)(3/5)=2/5.
- [1 mark] Thus P(at least one hit)=1−2/5=3/5.
- [1 mark] Exactly one hit has probability (1/3)(3/5)+(2/3)(2/5)=1/5+4/15=7/15.
- [0.5 marks] The answers are 3/5 and 7/15, respectively.
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