Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Probability · Very Long Answer5 Marksbayes_theorem

Class 12 Maths · Probability · Very Long Answer #77

Choose either bag with equal probability. Bag I has 5 red,3 black; II has 2 red,6 black. Draw two uniformly without replacement. Given both red, find P(bag I).
Two-red observation: bag-selection probability tree
Two-red observation: bag-selection probability tree

✅ Step-by-Step Solution

Final Answer: 10/11
  1. Let E be the observed event. The mutually exclusive exhaustive cases are I, II. Their prior probabilities are P(I)=1/2, P(II)=1/2.
  2. The conditional observation probabilities are P(E|I)=5/14, P(E|II)=1/28.
  3. By total probability, P(E)=(1/2)(5/14) + (1/2)(1/28)=11/56.
  4. The requested joint probability with E is 5/28=5/28.
  5. By Bayes’ theorem, the requested posterior is 5/28 / (11/56) = 10/11.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Let E be the observed event. The mutually exclusive exhaustive cases are I, II. Their prior probabilities are P(I)=1/2, P(II)=1/2.
  • [1 mark] The conditional observation probabilities are P(E|I)=5/14, P(E|II)=1/28.
  • [1 mark] By total probability, P(E)=(1/2)(5/14) + (1/2)(1/28)=11/56.
  • [1 mark] The requested joint probability with E is 5/28=5/28.
  • [1 mark] By Bayes’ theorem, the requested posterior is 5/28 / (11/56) = 10/11.

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
Choose uniformly among a two-headed coin, a coin with P(head)=3/4…
Next Question →
In a college, 60% of students are girls. Of boys 4% exceed 1.75 m in…

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).