Question

A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins.

Answer 1

Probability that A will win=> number of Favourable outcomes=6.
total number of outcomes=`36`
P (a will win)=`6/36=1/6`
P( a will not win)=`1-1/6=5/6`
Probability B will win=>number of favourable outcomes=`3`
P(B will win)=`3/36=1/12`
P(B will not win)=`11/12`
If A starts the game then B will only win if A fails everytime he throws......B can either win in the first round or second round or third or so on.,br> `(5/6)xx1/(12)+5/6xx11/12xx5/6xx1/12+5/6xx11/12xx5/6xx11/12xx5/6xx1/12...................................`so on
this is a infinite G.P with a=`5/72` and `r=55/72`
summation of infinite G.P=>`a/(1-r)=(5/72)/(1-55/72)=5/17`