A) 8/729
B) 8/243
C) 1/729
D) 8/9
Correct Answer: B
Solution :
[b] A pair of fair dice is thrown, the sample space \[S=(1,1),(1,2)(1,3)...=36\] Possibility of getting 9 are (5, 4), (4, 5), (6, 3), (3, 6) \[\therefore \] Possibility of getting score 9 in a single throw \[=\frac{4}{36}=\frac{1}{9}\] \[\therefore \]Probability of getting score 9 exactly twice \[{{=}^{3}}{{C}_{2}}\times {{\left( \frac{1}{9} \right)}^{2}}.\left( 1-\frac{1}{9} \right)=\frac{3!}{2!}\times \frac{1}{9}\times \frac{1}{9}\times \frac{8}{9}=\frac{8}{243}\]
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