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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????????/

6 years ago

Answers : (1)

AJIT AskiitiansExpert-IITD
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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Ajit Singh Verma IITD


 

6 years ago
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