Suppose you are answering a multiple-choice problem on a exam, and have to choose one ofn options (exactly one of which is correct). Let K = the event that you know the answer,and R = the event that you get the problem right. Suppose that if you know the right answer, you will definitely getthe problem right, but if you do not know, then you will guess completely randomly. LetP (K) = some probability p.(a) Find P (K|R) (in terms of p and n).(b) Prove that P (K|R) ≥ p, and give a more intuitive explanation for why thisis true.(c) When (if ever) does P (K|R) equal p?

Suppose you are answering a multiple-choice problem on a exam, and have to choose one ofn options (exactly one of which is correct). Let K = the event that you know the answer,and R = the event that you get the problem right. Suppose that if you know the right answer, you will definitely getthe problem right, but if you do not know, then you will guess completely randomly. LetP (K) = some probability p.(a) Find P (K|R) (in terms of p and n).(b) Prove that P (K|R) ≥ p, and give a more intuitive explanation for why thisis true.(c) When (if ever) does P (K|R) equal p?

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

Suppose you are answering a multiple-choice problem on a exam, and have to choose one of
n options (exactly one of which is correct). Let K = the event that you know the answer,
and R = the event that you get the problem right. Suppose that if you know the right answer, you will definitely get
the problem right, but if you do not know, then you will guess completely randomly. Let
P (K) = some probability p.
(a) Find P (K|R) (in terms of p and n).
(b) Prove that P (K|R) ≥ p, and give a more intuitive explanation for why this
is true.
(c) When (if ever) does P (K|R) equal p?

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