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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)

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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7 years ago
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