Two persons A and B throw a (fair) die (six faced cube faces numbered from 1 to 6 ) alternately, starting with. A the first person to get an outcome different from the pervious one by the opponent wins. The probability than B wins is

Options

A. `(5)/(6)`
B. `(6)/(7)`
C. `(7)/(8)`
D. `(8)/(9)`

Answer

B

Explanation

`P=(6)/(6)*(5)/(6)+(6)/(6)*(1)/(6)*(1)/(6)*(5)/(6)+(6)/(6)*(1)/(6)*(1)/(6)*(1)/(6)*(1)/(6)*(5)/(6)+....oo`
`=(5)/(6)+(5)/(6^(3))+(5)/(6^(5))+....`
`=(5//6)/(1-(1)/(36))=(30)/(35)=(6)/(7)`