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

Answer: (C)

$\frac{3}{715}$

Answer 2

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: $\frac{3}{715}$