A and B take turn in throwing two dice, the first to throw 9 being awarded. Show that if A has the first throw, thier chances of winning are in the ratio 9:8.

To win A should get (4,5) or (5,4) or (6,3) or (3,6)

p(A)=4/36=1/9

For B to win A must lose and B must win. Since independent :

p(B)=not(p(A))*1/9=(32/36)*(1/9)=(8/81)

=>

p(A)/p(B)=(1/9)/(8/81)=81/(8*9)=9:8