Probability
Bayes theorem with identical bags
nta_pyq_2025_apr
Grade 12
Question:
Given three indentical bags each containing 10 balls, whose colours are as follows : Red Blue Green Bag I 3 2 5 Bag II 4 3 3 Bag III 5 1 4 A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the balls is Green, the probability that it is from bag III is q , then the value of ( 1$p + 1$q ) is :
Step-by-Step Solution
Key Concept: Use Bayes theorem for bayes theorem with identical bags by writing the required posterior probability as a ratio of favourable conditional probabilities.
(3) 1 3 ( ) BI 3 10 1$p = P($) = = R 1 3 4 5 4 ( + + ) 3 10 10 10 1 4 ( ) BIII 3 10 1$q = ($) = = G 1 5 3 4 3 ( + + ) 3 10 10 10 1 1 ∴ + = 7 p q
Correct Answer: 3