True-false exam: A section of an exam contalns four true-false questions. A completed exam paper is selected at random, and the four answers are recorded. Round your answers to four decimal places if necessary. Part 1 of 3 Assuming the outcomes to be equally likely, find the probablity that all the answers are "False." The probability that all the answers are "False" is \( \square \) 0.0625 . Part: \( 1 / 3 \) Part 2 of 3 Assuming the outcomes to be equally likely, find the probability that exactly one of the four answers is "True." The probability that exactly one of the four answers is "True" is \( \square \) .

When dealing with a true-false exam consisting of four questions, each question has two outcomes: True (T) or False (F). The probability of any specific outcome (like all answers being False) is calculated by raising the number of outcomes to the power of the number of questions. In this case, since there are 2 outcomes for each of the 4 questions, the total number of possible outcomes is \( 2^4 = 16 \). Since the answers can be all True or all False, the probability of getting all False (FFFF) is \( 1/16 = 0.0625 \). Now, for exactly one answer being True, we need to find the combinations where one answer is True and the other three are False. This can happen in \( \binom{4}{1} = 4 \) ways (choosing which of the 4 questions is True). The probability for each specific combination (like TFFF) is \( 1/16 \), so the total probability of establishing exactly one True answer becomes \( 4/16 = 0.25 \).