Probability
Successive Draws Without Replacement
nta_pyq_2024_jan
Grade 12
Question:
An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability that the first draw gives all white balls and the second draw gives all black balls is:
$\dfrac{5}{256}$
$\dfrac{5}{715}$
$\dfrac{3}{715}$
$\dfrac{3}{256}$
Step-by-Step Solution
Key Concept: $P(\text{4W then 4B})=P(\text{4W from 15})\times P(\text{4B from remaining 11})=\frac{{}^6C_4}{{}^{15}C_4}\times\frac{{}^9C_4}{{}^{11}C_4}$.
$\frac{{}^6C_4\cdot{}^9C_4}{{}^{15}C_4\cdot{}^{11}C_4}=\frac{15\times126}{1365\times330}=\frac{3}{715}$.
Correct Answer: 3