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

Class 12 Maths · Probability · Very Long Answer #115

An insurer covers3000 scooters,4000 cars,5000 trucks. Their respective accident probabilities are0.02,0.03,0.04. Choose a uniform insured vehicle and condition on its having an accident. Find its probabilities of being a scooter,car,truck.

✅ Step-by-Step Solution

Final Answer: Scooter:3/19; car:6/19; truck:10/19.
  1. Let E be the observed event. The mutually exclusive exhaustive cases are scooter, car, truck. Their prior probabilities are P(scooter)=1/4, P(car)=1/3, P(truck)=5/12.
  2. The conditional observation probabilities are P(E|scooter)=1/50, P(E|car)=3/100, P(E|truck)=1/25.
  3. By total probability, P(E)=(1/4)(1/50) + (1/3)(3/100) + (5/12)(1/25)=19/600.
  4. The three accident joint weights are 3000·0.02 : 4000·0.03 : 5000·0.04 =60:120:200=3:6:10.
  5. Normalize the weights, whose sum is19: scooter probability=3/19, car=6/19, truck=10/19.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Let E be the observed event. The mutually exclusive exhaustive cases are scooter, car, truck. Their prior probabilities are P(scooter)=1/4, P(car)=1/3, P(truck)=5/12.
  • [1 mark] The conditional observation probabilities are P(E|scooter)=1/50, P(E|car)=3/100, P(E|truck)=1/25.
  • [1 mark] By total probability, P(E)=(1/4)(1/50) + (1/3)(3/100) + (5/12)(1/25)=19/600.
  • [1 mark] The three accident joint weights are 3000·0.02 : 4000·0.03 : 5000·0.04 =60:120:200=3:6:10.
  • [1 mark] Normalize the weights, whose sum is19: scooter probability=3/19, car=6/19, truck=10/19.

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
A lottery sells10000 tickets at ₹1 each. It awards one ₹3000 prize…
Next Question →
Bag A has3 red,5 black; B has4 red,4 black. Transfer2 uniform balls…

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).