1.

A tosses 2 fair coins & B tosses 3 fair cons after game is won by the person who throws greater number of heads. In case of a tie, the game is continued under identical rules until someone finally wins the game. The probability that A finally wins the game is K//11, then K is

Answer»


Solution :`A_(i)=` no. of heads obtained by `A` when tosses two coins
`B_(i)=` no of heads obtained by `B` when tosses `3` coins
`P(E)=P{(A_(1)nnB_(0))uu(A_(2)nnB_(2))uu(A_(2)nnB_(1))}`
`=2C_(1)(1/2)(1/2)(1/2)^(3)+(1/2)^(2)+(1/2)^(2)3C_(1)(1/2)(1/2)^(2)`
`=2/32+1/32+3/32=3/36`
`F={A` & `B` tie a PARTICULAR game `}`then`P(F)=P{(A_(0)nnB_(0))uu(A_(1)nnB_(1))uu(A_(2)nnB_(2))}=5/16`
`P` (`A` finally wins the game )
`=P(E` or `FE` or `FFE` or ........) `=3/11`


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