we throw 3 coins

y represents the throw of three coins
x represents the throw of the first two
we count the number of hetz gotten from the thrown coins.

the solution says for the slot that:
P(x=1,y=2)=0.25
but i cant understand how
?
the logical solution says:
for x to be 1 we have 01 10
so for y to be 2 011 101
so with respect to y we have two possibilities from 8

but the formal mathematical says

P(x=1,y=2)=P(x=1)*P(y=2/x=1)
for P(x=1) we need to have 01 10 which is 1/2 or 0.5
for P(y=2/x=1) its 2/8 or 0.25

P(x=1,y=2)=P(x=1)*P(y=2/x=1)=0.5*0.25=0.125
and not 0.25