A test contains 3 multiple-choice questions. Each question has 4 answers, out of which only one is correct. Suppose a student randomly selects an answer to each question, so that each of the possible responses are equally likely. Moreover, assume that in successively answering the questions, the student does not keep track of how previous questions were answered. Suppose the student will pass if at least 2 out of the 3 questions are answered correctly. What is the probability that the student will pass?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A test contains 3 multiple-choice questions. Each question has 4 answers, out of which only one is correct. Suppose a student randomly selects an answer to each question, so that each of the possible responses are equally likely. Moreover, assume that in successively answering the questions, the student does not keep track of how previous questions were answered.

Suppose the student will pass if at least 2 out of the 3 questions
are answered correctly. What is the probability that the student will pass?

 

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A test contains 3 multiple-choice questions. Each question has 4 answers, out of which only one is correct. Suppose a student randomly selects an answer to each question, so that each of the possible responses are equally likely. Moreover, assume that in successively answering the questions, the student does not keep track of how previous questions were answered.

Binomial distribution:

The binomial distribution gives the probability of number of successes out of n trials in a series of Bernoulli trials.

 

The probability mass function (pmf) of a binomial random variable X is given as:

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