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

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Solution

Q.
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 [2024]

1 $\frac{5}{715}$

2 $\frac{5}{256}$

3 $\frac{3}{715}$

4 $\frac{3}{256}$

Ans.
(3)

Let A : event when $1^{s t}$ draw gives all 4 white balls.

and B : event when $2^{n d}$ draw gives all 4 black balls.

$P (A) = \frac{{}^{6}{C_{4}}}{{}^{15}{C_{4}}} = \frac{1}{91}$ and $P (B | A) = \frac{{}^{9}{C_{4}}}{{}^{11}{C_{4}}} = \frac{21}{55}$

$∴$ $Required probability = P (A) \times P (\frac{B}{A}) = \frac{1}{91} \times \frac{21}{55} = \frac{3}{715}$

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