Math Problem Statement

Consider a multiple-choice test with five questions, each with four possible choices. As is usually the case, there is only one correct answer for each question (meaning that there are three incorrect answers for each question). Unfortunately, you didn’t study for this test, so you must resort to randomly guessing on each question. Let the discrete random variable X represent the number of questions you answer correctly. Consider this multiple-choice test as an experiment and consider each question as a Bernoulli trial. Explain how this situation satisfies all conditions of a Bernoulli trial.

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Bernoulli Trials
Binomial Distribution

Formulas

Probability of success for each question: p = 1/4
Probability of failure for each question: 1 - p = 3/4
Binomial probability formula: P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Theorems

Bernoulli Trial Theorem
Binomial Distribution Theorem

Suitable Grade Level

Grades 10-12