Probability
Bayes Theorem — Coins from Bags
nta_pyq_2024_apr
Grade 12
Question:
There are three bags $X$, $Y$ and $Z$. Bag $X$ contains 5 one-rupee coins and 4 five-rupee coins; Bag $Y$ contains 4 one-rupee coins and 5 five-rupee coins and Bag $Z$ contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag $Y$, is:
$\dfrac{1}{4}$
$\dfrac{1}{2}$
$\dfrac{5}{12}$
$\dfrac{1}{3}$
Step-by-Step Solution
Key Concept: Bayes: $P(Y|1\text{-rupee})=\frac{P(1|Y)P(Y)}{P(1|X)P(X)+P(1|Y)P(Y)+P(1|Z)P(Z)}$.
$P(Y|1\text{-rupee})=\frac{4}{5+4+3}=\frac{4}{12}=\frac{1}{3}$.
Correct Answer: 4