ProbabilityHardBloom L3
Question
A bag contains 6 white and 6 black balls. One by one the balls are drawn from the bag with replacement. Then the probability that 3rd time a white ball is drawn in 7th draw is
Options
A.$\frac{15}{64}$
B.$\frac{3}{64}$
C.$\frac{5}{128}$
D.$\frac{15}{128}$
Solution
Sol. [Key Concept: Bag 6W+6B drawn one by one: probability of the stated draw order.]
$$\therefore\ P = \frac{\ ^{n - 3}C_{m - 1}}{\ ^{n - 1}C_{m - 1}} = \frac{(n - m)(n - m - 1)}{(n - 1)(n - 2)}$$
$$P = \ ^{6}C_{2}\left( \frac{6}{12} \right)^{2}\left( \frac{6}{12} \right)^{4}\frac{6}{12} = \frac{15}{128}$$
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