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 of these
Correct Answer: A
Solution :
[a] The required event occurs if two sixes are observed in the first seven throws and a six is observed on the eight throw. If P is the probability that a six shows on the die, the number of throws n is 7, and X is the the number of times a six is observed, then \[X\tilde{\ }B(7,p).\] Therefore the required probability equals \[P(X=2)\] times the probability of getting a six on the eight throw, i.e., it equals \[{{(}^{7}}{{C}_{2}}{{p}^{2}}{{q}^{5}})(p)={{(}^{7}}{{C}_{2}}){{\left( \frac{1}{6} \right)}^{2}}{{\left( \frac{5}{6} \right)}^{5}}\left( \frac{1}{6} \right)=\frac{^{7}{{c}_{2}}({{5}^{5}})}{{{6}^{8}}}\]
You need to login to perform this action.
You will be redirected in
3 sec
