Question

Luc is playing a trivia game with multiple choice questions. he runs out of time and needs to guess on the last 2 questions. each question has 4 multiple choice options (1 of which is correct), so luc has a 1/4 probability of correctly guessing the answer to any given question. we categorize each guess as correct (c) or incorrect (i). here is a sample space showing the possible outcomes:

Answer 1

To find the probability that the student guesses more than 75 percent of the questions correctly on a 32-question multiple choice exam, we can use the binomial probability formula. After performing the calculations, the probability is approximately 0.4120 or 41.20%.

Step-by-step explanation:

In this question, the student is taking a 32-question multiple choice exam and randomly guessing each answer. Each question has three possible choices. To find the probability that the student guesses more than 75 percent of the questions correctly, we need to calculate the probability of guessing at least 25 out of 32 correctly. Let's use the binomial probability formula:
P(X ≥ k) = 1 - P(X < k)

P(guessed correctly) = 1/3, P(guessed incorrectly) = 2/3

Probability of guessing 25 or more correctly: P(X ≥ 25) = 1 - P(X < 25)
P(X < 25) = C(32, 1)(1/3)^1(2/3)^31 + C(32, 2)(1/3)^2(2/3)^30 + ... + C(32, 24)(1/3)^24(2/3)^8
By using a calculator or a computer program, we can evaluate this sum to find the probability.
After performing the calculations, we find that the probability is approximately 0.4120 or 41.20%.