Question 1047071
{{{p[3]=2p[1]}}},
{{{p[2]= 3p[3]}}},
{{{p[2] = p[4]}}},
{{{p[1]+p[2]+p[3]+p[4] = 1}}}

{{{p[2]= 3p[3]}}} ===> {{{p[3]= p[2]/3}}};

{{{p[3]=2p[1]}}} ===> {{{p[1] = p[3]/2 = p[2]/6}}};


===> {{{p[2]/6+p[2]+p[2]/3+p[2] = 1}}}

<===> {{{5p[2]/2 = 1}}}  ===> {{{p[2] = 2/5}}} 

===> {{{p[4] = 2/5}}}, {{{p[3] = 2/15}}}, and {{{p[1] = 1/15}}}.


Therefore {{{p[prime] = p[2]+p[3] = 2/5+2/15 = 8/15}}}