Question
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: \( 0 / 3 \) Part 1 of 3 Assuming the outcomes to be equally likely, find the probability that all the answers are "False." The probability that all the answers are "False" is
Ask by Dunn Cummings. in the United States
Feb 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that all four answers are "False" is 0.0625.
Solution
For each true-false question, there is a 1/2 chance of being "False." Since there are 4 independent questions, the probability that all are "False" is:
(1/2) × (1/2) × (1/2) × (1/2) = (1/2)^4 = 1/16 ≈ 0.0625.
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Simplify this solution The Deep Dive
To find the probability that all four answers are "False," we need to consider that each question has two possible outcomes: True (T) or False (F). Since there are four questions, the total number of possible answer combinations is \(2^4 = 16\). The outcome where all answers are "False" is just one specific combination (FFFF). Therefore, the probability \(P\) of all answers being "False" is: \[ P(\text{All False}) = \frac{1 \text{ (FFFF)}}{16 \text{ (total combinations)}} = \frac{1}{16} = 0.0625 \] So, the probability that all the answers are "False" is \(0.0625\).
