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)
The probability of getting a score less than $40$ by answering all the questions by guessing in this paper is

• A. $(\frac{1}{75}{)}^{10}$
• B. $1-(\frac{1}{75}{)}^{10}$
• C. $(\frac{74}{75}{)}^{10}$
• D. None of these

Answer 1

The correct option is B $1-(\frac{1}{75}{)}^{10}$

To get $40$ marks, he has to answer all questions correctly and its probability is $(\frac{1}{5}{)}^{10}(\frac{1}{15}{)}^{10}$.
Hence, probability of getting a score less than $40$ is
$1-(\frac{1}{5}{)}^{10}(\frac{1}{15}{)}^{10}=1-(\frac{1}{75}{)}^{10}$