Consider the events E1= Answer by student without guessing E2= Answer by student guessing A= At least three question correctly P(E1)=73,p(B2)=74p(E1A)=4C3(21)4+4C4(21)4=(21)4(4+1)=165p(E2A)=4C3(32)3×31+4C4(32)4=(32)3(34+32)p(E2A)=2716 Required probability =p(AE2)=p(E1)p(E1A)+p(E2)p(E2A)p(E2)p(E2A)=73×165+74×276474×2764=14291024