Probability
Bayes' Theorem
nta_pyq_2025_apr
Grade 12
Question:
Bag $B_1$ contains 6 white and 4 blue balls, Bag $B_2$ contains 4 white and 6 blue balls, and Bag $B_3$ contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability that the ball is drawn from Bag $B_2$ is:
$\frac{4}{15}$
$\frac{1}{3}$
$\frac{2}{5}$
$\frac{2}{3}$
Step-by-Step Solution
Key Concept: Apply Bayes' theorem: $P(B_2|W) = \frac{P(B_2)P(W|B_2)}{\sum_{i=1}^{3} P(B_i)P(W|B_i)}$.
$P(B_2|W) = \frac{\frac{1}{3}\cdot\frac{4}{10}}{\frac{1}{3}\cdot\frac{6}{10} + \frac{1}{3}\cdot\frac{4}{10} + \frac{1}{3}\cdot\frac{5}{10}} = \frac{4/30}{15/30} = \frac{4}{15}$.
Correct Answer: $\frac{4}{15}$