NCERT Class 12 · Ch 13 Exercise 13.1 · Q7
NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.1 Question 7
Two fair coins are tossed. Find P(E|F): (i) E=tail appears on one coin, F=one coin shows head; (ii) E=no tail, F=no 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: (i) 1 if “one coin” means exactly one; (ii) 0. If “one” means at least one in (i), the answer is 2/3.
- Use the equally likely ordered space {HH,HT,TH,TT}. In the exactly-one interpretation, both E and F are {HT,TH}, hence P(E|F)=1.
- In (ii), E={HH}, F={TT}, so E∩F is empty and the conditional probability is 0.
- Under the alternate at-least-one reading in (i), E={HT,TH,TT}, F={HH,HT,TH}; two of three conditioned outcomes qualify, giving 2/3.
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