Probability
Bayes' Theorem — Two Bags
nta_pyq_2024_jan
Grade 12
Question:
Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag $A$, if the ball drawn is white, is:
$\dfrac{1}{4}$
$\dfrac{1}{9}$
$\dfrac{1}{3}$
$\dfrac{3}{10}$
Step-by-Step Solution
Key Concept: Bayes: $P(A|W)=\frac{P(A)P(W|A)}{P(A)P(W|A)+P(B)P(W|B)}=\frac{\frac{1}{2}\cdot\frac{3}{10}}{\frac{1}{2}\cdot\frac{3}{10}+\frac{1}{2}\cdot\frac{3}{5}}$.
$P(A|W)=\frac{3/10}{3/10+6/10}=\frac{1}{3}$.
Correct Answer: 3