NCERT Class 12 · Ch 13 Exercise 13.3 · Q13
NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.3 Question 13
A speaks truth with probability 4/5. A fair coin is tossed and A reports head. Find P(actual head|report head).
💡 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: A: 4/5 under the symmetric truthful/false reporting model.
- Assume the report is always H or T and accuracy 4/5 is the same for either actual outcome. Then P(report H|H)=4/5 and P(report H|T)=1/5.
- Bayes gives [(1/2)(4/5)]/[(1/2)(4/5)+(1/2)(1/5)]=4/5. A mere unconditional truth frequency without this reporting assumption would not determine the posterior.
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