Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Probability · Long Answer3 Marksconditional_probability

Class 12 Maths · Probability · Long Answer #54

Two children are independently equally likely to be boys or girls. Find P(both girls) given (i) youngest is a girl; (ii) at least one is a girl.

✅ Step-by-Step Solution

Final Answer: (i) 1/2; (ii) 1/3
  1. Use ordered birth sequences BB,BG,GB,GG, each of probability 1/4.
  2. Given youngest is a girl, only BG,GG remain and only GG has both girls, so probability=1/2.
  3. Given at least one girl, the possible sequences are BG,GB,GG; one is GG, so probability=1/3.
  4. The two conditional probabilities are 1/2 and 1/3, respectively.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Use ordered birth sequences BB,BG,GB,GG, each of probability 1/4.
  • [1 mark] Given youngest is a girl, only BG,GG remain and only GG has both girls, so probability=1/2.
  • [1 mark] Given at least one girl, the possible sequences are BG,GB,GG; one is GG, so probability=1/3.
  • [0.5 marks] The two conditional probabilities are 1/2 and 1/3, respectively.

Master Chapter 13: Probability

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Probability.
📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →
← Previous Question
Independent A,B satisfy P(A∩B′)=1/4 and P(A′∩B)=1/6. Find all…
Next Question →
Uniformly select a committee of 4 from 7 boys and 4 girls. Given at…

More Practice Questions in Probability

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

Related Questions in Probability

Class 12 Probability · Mcq Single Correct
Given P(A)=4/5 and P(A∩B)=7/10, find P(B|A).
Class 12 Probability · Mcq Single Correct
Five independent fair coins are tossed. Find the probability of at least one head.
Class 12 Probability · Mcq Single Correct
Given P(A|B)=0.3, P(A)=0.4, P(B)=0.8, find P(B|A).
Class 12 Probability · Mcq Single Correct
Two independent fair dice have sum 9. Find the conditional probability that at least one die…
Class 12 Probability · Mcq Single Correct
Choose an ordered pair (a,b) uniformly with distinct a,b from {1,2,3,4,5}. Find P(a/b is an…
Class 12 Probability · Mcq Single Correct
Given P(A)=0.4, P(B)=0.3 and P(A∪B)=0.5, find P(B′∩A).