A) \[^{7}{{C}_{2}}\frac{{{5}^{5}}}{{{6}^{8}}}\]
B) \[^{7}{{C}_{3}}\frac{{{5}^{3}}}{{{6}^{8}}}\]
C) \[^{7}{{C}_{6}}\frac{{{5}^{6}}}{{{6}^{8}}}\]
D) None
Correct Answer: A
Solution :
The required event occurs if two sixes are observed in the first seven throws and a six is observed on the eighth throw. If p is the probability that a six shows on the die, the number of throws n is 7, and X is the number of times a six is observed, then X \[\sim \] B(7,p). Therefore the required probability equals P(X = 2) times the probability of getting a six on the eighth throw, i.e., it equals \[{{(}^{7}}{{C}_{2}}{{p}^{2}}{{q}^{5}})(p)={{(}^{7}}{{C}_{2}}){{\left( \frac{1}{6} \right)}^{2}}{{\left( \frac{5}{6} \right)}^{5}}\left( \frac{1}{6} \right)\]\[=\frac{^{7}{{C}_{2}}({{5}^{3}})}{{{6}^{8}}}\]
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