NCERT Class 12 · Ch 13 Exercise 13.2 · Q14
NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.2 Question 14
A,B solve a problem independently with probabilities 1/2,1/3. Find (i) P(problem solved), (ii) P(exactly one solves).
💡 Concept Hints
- Define the events and identify which event is being conditioned on.
- Use P(E|F)=P(E∩F)/P(F), or separate the possible sources before applying total probability and Bayes.
✅ Step-by-Step Solution
Final Answer: (i) 2/3; (ii) 1/2.
- (i) Complement of both failing: 1−(1−1/2)(1−1/3)=1−1/3=2/3.
- (ii) Add disjoint possibilities: (1/2)(2/3)+(1/2)(1/3)=1/3+1/6=1/2.
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