A and B take turns in throwing two dice, the first to throw 9 being awarded the prize. Show that their chance of winning are in the ratio 9:8.

Explanation

According to question :

Total number of events =36

`P( getting 9)=frac{4}{36}=frac{1}{9}`

P( A winning )=P( getting 9 in first throw )+P(g etting 9 in third throw )+..



`=frac{1}{9}+(1-frac{1}{9})(1-frac{1}{9}) times frac{1}{9}+ldots `

`=frac{1}{9}[1+frac{64}{81}+(frac{64}{81})^{2}+ldots. `

...