Question

In an objective paper, there are two sections of $10$ questions each. For "section $1$", each question has $5$ options and only one option is correct and "section $2$" has $4$ options with multiple answers and marks for a question in this section is awarded only if he ticks all correct answers. Marks for each question in "section $1$" is $1$ and in "section $2$" is $3.$
(There is no negative marking)
If a canidate attempts only two questions by guessing, one from "section $1$" and one from "section $2$", the probability that he scores in both questions is

• A. $\frac{74}{75}$
• B. $\frac{1}{25}$
• C. $\frac{1}{15}$
• D. $\frac{1}{75}$

Answer 1

The correct option is D $\frac{1}{75}$

Let $p_1$ be the probability of being an answer correct from section $1$. Then $p_1=\frac{1}{5}.$ Let $p_2$ be the probability of being an answer correct from section 2. Then $p_2=\frac{1}{15}$. Hence, the recquired probability is $\frac{1}{5}\times \frac{1}{15}=\frac{1}{75}$.