(1/2)^3*4=1/2???shoud be4* (1/2)^3*(1/2)=1/4,1-,,,=9/16

Second time 0: P(E0)=C(4,0)*(2/3)^4*(1/3)^0=16/81
Second time 1: P(E1)=C(4,1)*(2/3)^3*(1/3)^1=32/81
The answer P(E)=[(16/81)*(9/16)+(32/81)*(7/8)]/[16/81+32/81]=37/48
Please check it.
Thank you,let me review Bernoulli formula and Prob. Tree.