Answer to Question #186935 in Statistics and Probability for Ashwini

Question #186935

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


1
Expert's answer
2021-05-07T09:50:48-0400

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

a) P(A)=C(6,4)C(15,4)C(9,4)C(15,4)=1513651261365=0.0010=0.1%\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) P(B)=C(6,4)C(15,4)C(9,4)C(11,4)=151365126330=0.0042=0.42%\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\%


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