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Probability
NCERT Class 12
CBSE
Grade 12

Question:

Bag I contains 3 red and 4 black balls while Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag II.

Step-by-Step Solution

$P(E_1)=P(E_2)=1/2, P(A|E_1)=3/7, P(A|E_2)=5/11$. [1.0 Mark]
Bayes' formula: $\dfrac{5/11}{3/7 + 5/11}$. [1.0 Mark]
$= \dfrac{35}{68}$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Identifying conditional probabilities: 1.0 Mark
Applying Bayes' theorem formula: 1.0 Mark
Evaluating probability $= 35/68$: 1.0 Mark

Correct Answer:
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