Question

a student ran out of time on a multiple choice exam and randomly guess the answers for two problems each problem have four answer choices ABCD and only one correct answer what is the probability that he answered neither of the problems correctly ​

Answer 1

The probability that a student answers neither of the two multiple choice questions correctly, when each question has four answer choices, is 56.25%.

Step-by-step explanation:

The subject of this question is Mathematics, specifically dealing with probability. The student is asking about the likelihood of randomly guessing on a multiple choice exam with four answer choices per question and getting neither question correct. To calculate this, we need to consider the probability of getting a question wrong, which is ¾ or 0.75 since there are three incorrect answers out of four possible choices. The probability of getting both questions wrong is the product of the probabilities of getting each question wrong:

• P(getting the first question wrong) = ¾ = 0.75
• P(getting the second question wrong) = ¾ = 0.75

Therefore, the probability of getting both questions wrong is:

P(both questions wrong) = P(first question wrong) × P(second question wrong) = 0.75 × 0.75 = 0.5625

So the probability that the student answers neither of the problems correctly is 56.25%.