Question

If a student is randomly choosing the answer to each of four true-false questions in a test, what is the probability that all his answers are correct (write up to the fourth decimal place)?

Answer 1

To determine the probability that all his answers are correct:

Let the probability of choosing the answer true in the test be $\frac{1}{2}$.

The probability of not choosing the answer true in the test be $1-\frac{1}{2}=\frac{1}{2}$.

The number of times, student have to choose the answers are $4$.

The probability that in all four questions, all his answers are correct is as:

$\begin{array}{rcl}\mathrm{Probability}& =& {\left(\frac{1}{2}\right)}^4\\ & & \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\\ & =& \frac{1}{16}\\ & =& 0.0625.\end{array}$

Therefore, the probability that all his answers are correct is $0.0625$.