Probability
Conditional Probability — Drawing from Bag after Die Roll
nta_pyq_2023_apr
Grade 12
Question:
A bag has 6 white and 4 black balls. A die is rolled; $n$ balls are drawn equal to the die's number. $P$(all drawn balls are white) is
Step-by-Step Solution
Key Concept: $P=\frac{1}{6}\sum_{k=1}^{6}\frac{\binom{6}{k}}{\binom{10}{k}}$. Compute each term: $\frac{6}{10}+\frac{15}{45}+\frac{20}{120}+\frac{15}{210}+\frac{6}{252}+\frac{1}{210}$.
$P=\frac{1}{5}$.
Correct Answer: 3