2D probability question..

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