Probability of getting all four answers right, with true and false in each question

For each of the four questions, there are two possible outcomes. Thus, in total, there are $2^4 = 16$ ways to answer the four questions.
\begin{array}{c c c c} T & T & T & T\\ T & F & T & T\\ T & T & F & T\\ T & F & F & T\\ T & T & T & F\\ T & F & T & F\\ T & T & F & F\\ T & F & F & F\\ F & T & T & T\\ F & F & T & T\\ F & T & F & T\\ F & F & F & T\\ F & T & T & F\\ F & F & T & F\\ F & T & F & F\\ F & F & F & F \end{array}

Only one of these $16$ sequences is correct. Assuming each of these $16$ sequences is equally likely to occur (as would result from random guessing), the probability that all four questions are answered correctly is $1/16$.

If we assume that a person is equally likely to guess true or false on each question, then he or she has probability $1/2$ of answering each question correctly. Under the assumption of independence, the probability that all four questions are answered correctly is $$\left(\frac{1}{2}\right)^4 = \frac{1}{16}$$ We add probabilities of mutually exclusive events (events that cannot occur at the same time). We multiply probabilities of independent events.

So the most direct way of telling you what the answer is is this:

For each question you have 1/2 chance of getting the right answer.

Since there are four questions, each has a 1/2 chance of getting the right answer. So to find it, you do (1/2)x(1/2)x(1/2)x(1/2). Therefore, for this case, there is a 1/16 chance of getting the right answer or (1/(2^4)) chance. Or a 6.25% chance.