# 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 at least four questions, is

Firstly, probability of getting exactly 4 correct answers =3 correct MCQ and a T/F+2 correct MCQ and 2 T/F.

$$\Rightarrow \frac{1}{4} \cdot \frac{1}{4} \cdot \frac{1}{4} \cdot\left(\begin{array}{l} 2 \\ 1 \end{array}\right) \cdot \frac{1}{2} \cdot \frac{1}{2}+\left(\begin{array}{l} 3 \\ 2 \end{array}\right) \cdot \frac{1}{4} \cdot \frac{1}{4} \cdot \frac{3}{4} \cdot \frac{1}{2} \cdot \frac{1}{2}=\frac{11}{256}\\ \text { The probability of getting exactly } 5 \text { correct answers }=\frac{1}{4} \cdot \frac{1}{4} \cdot \frac{1}{4} \cdot \frac{1}{2} \cdot \frac{1}{2}=\frac{1}{256}\\ \text { Total probability }=\frac{11}{256}+\frac{1}{256}=\frac{3}{64}$$