P(z=0)=1/2*1/3=1/6
P(z=1)=1/2*2/3+3/8*1/3=11/24
P(z=2)=3/8*2/3=1/4
P(z=3)=1/8*1/3=1/24
P(z=4)=1/8*2/3=1/12
z 0 1 2 3 4
P 1/6 11/24 1/4 1/24 1/12
P(z=0)=1/2*1/3=1/6
P(z=1)=1/2*2/3+3/8*1/3=11/24
P(z=2)=3/8*2/3=1/4
P(z=3)=1/8*1/3=1/24
P(z=4)=1/8*2/3=1/12
z 0 1 2 3 4
P 1/6 11/24 1/4 1/24 1/12