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:

• A. \( \frac{5}{256} \)
• B. \( \frac{2}{715} \)
• C. \( \frac{3}{715} \)
• D. \( \frac{3}{256} \)

Answer 1

The Correct Option is C

Probability of drawing 4 white balls in the first draw:
\(\frac{\binom{6}{4}}{\binom{15}{4}} = \frac{15}{1365}.\)

After removing 4 white balls, there are 9 black balls left. Probability of drawing 4 black balls in the second draw:  
\(\frac{\binom{9}{4}}{\binom{11}{4}} = \frac{126}{330}.\)

The required probability is:  
\(\frac{15}{1365} \times \frac{126}{330} = \frac{3}{715}.\)

The Correct answer is: \( \frac{3}{715} \)