Question

As a part of a probability experiment, Sachin is told to answer $4$ multiple-choice questions. For each question, there are $3$ choices out of which only $1$ is correct. If Sachin randomly and independently answers each question, what is the probability that he will answer the $4$ questions correctly?

• A. $\frac{27}{81}$
• B. $\frac{12}{81}$
• C. $\frac{4}{81}$
• D. $\frac{3}{81}$
• E. $\frac{1}{81}$

Answer 1

The correct option is E $\frac{1}{81}$

There are $3$ options for each question and only one is correct.

Hence, the probability of getting a question correct is $=\frac{1}{3}$. Now, he has attempted $4$ questions.

Thus the probability of getting all the four right is
$=\left(\frac{1}{3}\right)\times \left(\frac{1}{3}\right)\times \left(\frac{1}{3}\right)\times \left(\frac{1}{3}\right)=\frac{1}{3^4}=\frac{1}{81}$