NCERT Class 12 · Ch 13 Exercise 13.3 · Q6
NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.3 Question 6
Choose equally among a two-headed coin, a 75%-heads coin and a fair coin. A head occurs. Find P(two-headed coin|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: two-headed: 4/9
- Use the mutually exclusive source events with prior probabilities two-headed=1/3, biased=1/3, fair=1/3.
- The observation likelihoods in the same order are 1, 3/4, 1/2. Multiply each prior by its likelihood to get joint probabilities 1/3, 1/4, 1/6.
- Total probability of the observation is 1/3 + 1/4 + 1/6 = 3/4.
- Bayes: P(two-headed | observation) = 1/3 / 3/4 = 4/9.
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