A and B are playing a dice game with one dice. A starts the game first. 6 will win. What is
the probability that A will win the game?
I found the answer by the help of 1/1-n,using series and limit. The answer is 6/11. But there is another solution and I can't understand the logic of it.The solution is as follows:
A starts first.The probability that A will win is "x".
The probability that B will win is 5
-----.x
6
x + (5/6)x= 1 x=6/11
There is also another solution:
x= (1/6)(1) + (5/6)(5/6)u
x[1 - 25/36] = 1/6
x(11/36) = 1/6
x = 6/11
In the second alternative solution I think they mean this. A either wins on first throw or wins but not on first throw. For first throw p=1/6. For not on first throw
p=(5/6)(5/6)x (This is because after A and B have failed on first throw its like starting a new match so probability of A winning overall is still x)
So x=(1/6)+(5/6)(5/6)x