A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $$9$$ twice is :
JEE · Math · previous-year question
- A.$$8/729$$
- B.$$8/243$$correct
- C.$$1/729$$
- D.$$8/9.$$
Answer
B. $$8/243$$
Explanation
Probability of getting score 9 in a single throw $$ = {4 \over {36}} = {1 \over 9}.$$ Probability of getting score 9 exactly twice $$ = {}^3{C_2} \times {\left( {{1 \over 9}} \right)^2} \times {8 \over 9} = {8 \over {243}}.$$
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