An objective type test paper has 5 questions, Out of these 5 questions, 3 questions have four options each (A, B, C, D) with one option being the correct answer. The other 2 questions have two options each, namely true and false. A candidate randomly ticks the options. Then the probability that he/she will tick the correct option in atleast four questions is

Case (i) : 4 correct + 1 incorrect. For correct answer, he/she has to tick the correct option only, while for incorrect answer, he/she can give wrongly in 3 ways for $1^{st}$ three questions each and in 1 way each for last 2 questions.

$\therefore \text{ Required Probability }=\frac{3+3+3+1+1}{4\times 4\times 4\times 2\times 2}=\frac{11}{256}$

Case (ii) : All 5 correct

$\text{ Probability }=\frac{1}{4\times 4\times 4\times 2\times 2}=\frac{1}{256}$

$\therefore \text{ Required probability }=\frac{11}{256}+\frac{1}{256}=\frac{12}{256}=\frac{3}{64}$