Class 12 Probability · Long Answer3 Marksbayes_theorem

Class 12 Maths · Probability · Long Answer #105

Choose bags X,Y with equal probability. X contains4 white,2 black; Y contains3 white,3 black. Draw two uniformly without replacement. Given one white and one black, find P(bag Y).

✅ Step-by-Step Solution

Final Answer: 9/17

Let E be the observed event. The mutually exclusive exhaustive cases are X, Y. Their prior probabilities are P(X)=1/2, P(Y)=1/2.
The conditional observation probabilities are P(E|X)=8/15, P(E|Y)=3/5. By total probability, P(E)=(1/2)(8/15) + (1/2)(3/5)=17/30.
The requested joint probability with E is 3/10=3/10.
By Bayes’ theorem, the requested posterior is 3/10 / (17/30) = 9/17.

📋 CBSE Stepwise Marking Scheme

[0.5 marks] Let E be the observed event. The mutually exclusive exhaustive cases are X, Y. Their prior probabilities are P(X)=1/2, P(Y)=1/2.
[1 mark] The conditional observation probabilities are P(E|X)=8/15, P(E|Y)=3/5. By total probability, P(E)=(1/2)(8/15) + (1/2)(3/5)=17/30.
[1 mark] The requested joint probability with E is 3/10=3/10.
[0.5 marks] By Bayes’ theorem, the requested posterior is 3/10 / (17/30) = 9/17.

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Class 12 Maths · Probability · Long Answer #105

✅ Step-by-Step Solution

📋 CBSE Stepwise Marking Scheme

Master Chapter 13: Probability

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