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abhishek dwivedi Grade: 12
`        A,B,C in order toss a coin. the one to throw a head wins.what are their respective chances of winning assuming that the game may continue indefinetely????????/`
7 years ago

## Answers : (1)

68 Points
```										Dear  abhishek ,
let the event a THROWS HEAD be denoted by A , not win( THROW A TAIL) by A'. similar for B and C. sp , P(A) =P(A') =1/2 and same for b and c.
P( Awin) = P( A wins in first turn ) + P( A wins in two turns ) +P( A wins in three turns ) +..........  ad.infinity
P(Awin)  = P(A) + P(A'B'C'A) +P( A'B'C'A'B'C'A).....
P(Awin) =  1/2 + (1/2 )^4 + (1/2)^7....
P(Awin) = (1/2)/(1-(1/2)^3)  = 4/7
P(B wins) = P(A'B) + P(A'B'C'A'B) +P(A'B'C'A'B'C'A'B)+........
P(BWINS) = (1/2)^2 + (1/2)^5 +(1/2)^8.....
P(B wins) = 2/7
similarly , P(C wins) = 1/7
hope it helps !!!!

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