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 = theevent 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) = someprobability 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?
n options (exactly one of which is correct). Let K = the
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
(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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