two person Aand B throw a coin alternatevely till one of them gets ' head' and wins the game. find the respective probabilities of winning
33AH AT BH BT are A gets Head, A gets tail, B gets Head, B gets tail respectively..
req prob of A winning
=AH+AT.BT.AH+AT.BT.AT.BT.AH+
(1/2)+(1/2*1/2*1/2)+(1/2*1/2*1/2*1/2*1/2)+..............
= (1/2) =2/3
(1/4-1)
Prob of B winning
=AT.BH+AT.BT.AT.BH+....
=(1/2*1/2)+(1/2*1/2*1/2*1/2)+..
=(1/4) =1/3 ..... also P(B winning)=1-P(A winning)=1-2/3=1/3
(1/4-1)
33Okie..
A can win if A gets head...
Now A gets Head on first throw...or A gets tail then B gets tail(if B gets tail here he wins..)then A gets head... or AT BT AT BT Ah..+ and so on......till A gets head...
thats infinite GP..
Similarly for B to win..
62This is much simpler by reccursion
A is Event that A Wins
B is Event that B Wins
thus,
P(A)=1/2+ (1/2)(1/2). P(A) (WHy?)
thus P(A)=2/3
33A is a winning
B is B winning
[7]
mere ko thik se samjh me nahi aaya...
