Probability
Bayes Theorem — Balls from Urns
nta_pyq_2024_apr
Grade 12
Question:
Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn A is:
$\dfrac{5}{18}$
$\dfrac{5}{16}$
$\dfrac{4}{17}$
$\dfrac{7}{18}$
Step-by-Step Solution
Key Concept: Apply Bayes' theorem. $P(\text{black})=\frac{1}{3}\left(\frac{5}{12}+\frac{7}{12}+\frac{6}{12}\right)$. $P(A|\text{black})=\frac{\frac{1}{3}\cdot\frac{5}{12}}{\frac{1}{3}\cdot\frac{18}{12}}$.
$P(A|\text{black})=\frac{5/12}{5/12+7/12+6/12}=\frac{5}{18}$.
Correct Answer: 1