What is the probability that the student does not know the answer and still chooses the correct answer? (b) What is the probability that the student responds correctly? (c) What is the probability that the student did not know the answer given that the student answered it correctly?

What is the probability that the student does not know the answer and still chooses the correct answer? (b) What is the probability that the student responds correctly? (c) What is the probability that the student did not know the answer given that the student answered it correctly?

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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Question

A student responds to a multiple choice question in an exam. The question has 4 choices and only one of the choices is the correct answer. Suppose that the probability that the student knows the correct answer is 0.8. Let us assume that when the student knows the correct answer the student answers the question correctly (i.e., selecting a wrong choice by mistake cannot happen). Furthermore, let us assume that when the student does not know the correct answer, the student does not leave the question unanswered, instead the student then guesses one of the 4 choices at random.
(a) What is the probability that the student does not know the answer and still chooses the correct answer?
(b) What is the probability that the student responds correctly?
(c) What is the probability that the student did not know the answer given that the student answered it correctly?

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