Question

A bag contains 6 white and 9 black balls . Four balls are drawn at a time .Find the probability for the first draw to give four white and second draw to give four black balls in each of the following cases:

a) The balls are replaced before the second draw.

b) The balls are not replaced before the second draw

Answer 1

Two draws are independent events, so the probabilities of the individual draws will multiply.

a) $\displaystyle P(A) = \frac{C(6,4)}{C(15,4)} \cdot \frac{C(9,4)}{C(15,4)} = \frac{15}{1365} \cdot \frac{126}{1365} =0.0010 = 0.1\%$

b) $\displaystyle P(B) = \frac{C(6,4)}{C(15,4)} \cdot \frac{C(9,4)}{C(11,4)} = \frac{15}{1365} \cdot \frac{126}{330} =0.0042 = 0.42\%$