From state

to state

in $M$ rounds

$P\left(i\mathrm{,}j\mathrm{,}M\right)$

$i=3$

$j=0$

$M=1$

$P\left(3,0,1\right)=0$

$i=3$

$j=0$

$M=2$

$P\left(3,0,2\right)=0$

$i=3$

$j=0$

$M=3$

$P\left(3,0,3\right)=0$

$i=2$

$j=0$

$M=1$

$P\left(2,0,1\right)=0$

$i=2$

$j=0$

$M=2$

${\left(1-p\right)}^2$

$i=2$

$j=0$

$M=3$

${\left(1-p\right)}^2\cdot 1+{\left(1-p\right)}^3\cdot p$

$i=2$

$j=0$

$M=4$

${\left(1-p\right)}^2\cdot 1^2+{\left(1-p\right)}^3\cdot p$