A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is (1) 1/729 (2) 8/9 (3) 8/729 (4) 8/243

Options

A. `8//9`
B. `7//29`
C. `8//243`
D. `1//729`

Answer

C

Explanation

Possiblities of getting 9 are `(5,4),(4,5),(6,43),(3,6).`
`thereforep=(4)/(36)=1/9andq=1-1/9=8/9`
Therefore, the required probability is
`""^(3)C_(2)q^(1)p^(2)=(3)((8)/(9))((1)/(9))^(2)=(8)/(143)`