Question

As part of a probability experiment, Elliott is to answer $4$ multiple-choice questions. For each question, there are $3$ possible answers, only $1$ of which is correct. If Elliott 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 4 questions with 3 possible choices for each question so

there are $3^4$ possible outcomes.

Only one of the outcomes is the one with all four choices correct so,

$p=\frac{1}{3^4}=\frac{1}{81}$