A quiz consists of 3 multiple choice questions, each of which have 10 answer choices. You are allowed three attempts at the quiz. What is the probability that someone would end up with a perfect score for the quiz simply by guessing the answers?
To calculate the probability of getting a perfect score by guessing, we need to find the probability of guessing all three questions correctly.
Since each question has 10 answer choices, the probability of guessing the correct answer for each question is 1/10. Therefore, the probability of guessing all three questions correctly is:
P(guessing all three correctly) = (1/10) * (1/10) * (1/10) = 1/1000 = 0.001
However, you have three attempts at the quiz. This means that you have three opportunities to guess all three questions correctly.
To find the probability of getting a perfect score in any of the three attempts, we need to subtract the probability of not getting a perfect score from 1.
P(not getting a perfect score) = 1 - P(guessing all three correctly) = 1 - 0.001 = 0.999
Since you have three attempts, the probability of getting a perfect score by guessing is:
P(getting a perfect score) = 1 - P(not getting a perfect score) in all three attempts
= 1 - (0.999 * 0.999 * 0.999)
= 1 - 0.997001
= 0.002999
Therefore, the probability that someone would end up with a perfect score for the quiz simply by guessing the answers is approximately 0.002999 or 0.3%.
To calculate the probability of getting a perfect score on the quiz by guessing, we first need to determine the probability of guessing one question correctly.
For each question, there are 10 answer choices and only one correct answer. Therefore, the probability of guessing the correct answer to one question is 1/10.
Since there are three questions in the quiz and you have three attempts, we can calculate the probability of getting a perfect score by multiplying the probabilities of guessing each question correctly together.
P(guessing all three questions correctly) = P(question 1 correctly) * P(question 2 correctly) * P(question 3 correctly)
= (1/10) * (1/10) * (1/10)
= 1/1000
So, the probability of someone getting a perfect score on the quiz simply by guessing the answers is 1/1000 or 0.001 (0.1%).
Please note that this calculation assumes that the questions are independent of each other, and that each guess for each question has an equal probability of being correct.