A and B throw a die alternatively till one of them gets a '6' and wins the game. find their respective probablilites of winning, if A syarts first.

Given:A and B throw a dice simultaneously till one thus gets a 6 and wins this game.

Now, consider winning of A

Let S and F be the following events.

S: obtaining a six by A

F: not obtaining a six by B

A can win the following way:

(i) He obtains a six in the first trial

(ii) A fails to obtain a six, B fails to obtain and then A obtains a six

(iii) A fails, then B fails, then A fails, then B fails to obtain and finally A obtains a six and so on

Obtaining a six by A and not obtaining a six by B are independent events