Probablity student knows the answer, P(A)=34
Probablity student knows the answer, P(B)=14
Probablity of correct answer when student knows the answer, P(CA)=1
Probablity of correct answer when student guesses the answer, P(CB)=14
So, probablity student gives answer correctly, when he knows the answer,
P(AC)=P(A)⋅P(CA)P(A)⋅P(CA)+(P(B)⋅P(CB))
=34⋅1(34)+(14)(14)=341316=1213