Question #1: He eliminated 1 of the 3 choices. So the probability of getting correct answer is 1/2.
Question #2: He eliminated 1 of the 3 choices. So the probability of getting correct answer is 1/2.
For Question #3-5: The probability of getting correct answer is 1/3 and getting incorrect it 2/3.
He should get at least 2 out of 3 correctly answered. The probability would be :-
P(at least 2 correct out of 3) = P(exactly 2 correct) + P(all 3 correct)
[tex]Probability=C(3,2)*(\frac{1}{3} )^{2} *(\frac{2}{3} ) + C(3,3)*(\frac{1}{3} )^{3} \\\\
Probability=3*(\frac{1}{9}) *(\frac{2}{3} ) + 1*(\frac{1}{27} ) \\\\
Probability=\frac{6}{27}+\frac{1}{27} \\\\
Probability=\frac{6+1}{27}=\frac{7}{27}[/tex]
Combined probability would be = [tex]\frac{1}{2} *\frac{1}{2}* \frac{7}{27} =\frac{7}{108}[/tex]
