You take a three question true-or-false quiz. You guess on all the questions. What is the probability that you will get a perfect score?
(1/2)^3
To calculate the probability of getting a perfect score on a three-question true-or-false quiz where you guess on every question, we first need to determine the probability of correctly guessing each question.
In a true-or-false quiz, there are two possible answers: true or false. When you guess on a question, you have a 50% chance of getting it right and a 50% chance of getting it wrong.
So, the probability of guessing a single question correctly is 1/2 or 0.5.
Since you are guessing on each of the three questions, the probability of getting all three questions right is calculated by multiplying the probability of getting each question right:
P(perfect score) = P(correct guess) * P(correct guess) * P(correct guess)
P(perfect score) = 0.5 * 0.5 * 0.5
P(perfect score) = 0.125
Therefore, the probability of getting a perfect score by guessing on all three true-or-false questions is 0.125 or 12.5%.