A and B throw a die alternatively till one of them gets a 6 and wins t

1.	A and B throw a die alternatively till one of them gets a 6 and wins thegames. Find their respective probability of winning, if A starts first.
Answer» Given:A and B throw a dice simultaneously till one thus gets a 6 and wins this game. Now, consider winning of A LetSandFbe 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 P(A wins)=P(S)+P(FFS)+P(FFFFS)=1/6+1/6(5/6)^2+1/6(5/6)^2=1/6*(1/1-5/6)^2)=1/6/1-25/36=6/11

A and B throw a die alternatively till one of them gets a 6 and wins thegames. Find their respective probability of winning, if A starts first.

Answer»

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

Now, consider winning of A

LetSandFbe 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

P(A wins)=P(S)+P(FFS)+P(FFFFS)=1/6+1/6*(5/6)^2+1/6*(5/6)^2=1/6*(1/1-5/6)^2)=1/6/1-25/36=6/11